Maths-
General
Easy
Question
Factor out the GCF from the given polynomial.

Hint:
- The highest number that divides exactly into two or more numbers is known as GCF.
- A polynomial is a type of algebraic expression in which the exponents of all variable should be a whole number.
The correct answer is: So, The GCD of this polynomial will be x.
- We have been given a polynomial in the question
- We have to factor out the GCF of the given polynomial.
Step 1 of 1:
We have to find the GCD of the given polynomial
.
Now we will factorize the given polynomial and extract the greatest factor from it.
So,


So, The GCD of this polynomial will be x.
So, The GCD of this polynomial will be x.
Related Questions to study
Maths-
Solution:
Hint:
We have a given figure

In this figure,

4x = 20
x = 50
So,

= 150
And

7(5) - 20
= 150
Now, we know that the sum of angle of triangle is 1800.
So,




Hint:
- the base angle theorem states that if the sides of a triangle are congruent then the angles opposite these sides are congruent.
- We have been given in the question diagram of a triangle named ABC where ∠ABC=60.
- We have to find out angle A.
We have a given figure
In this figure,
4x = 20
x = 50
So,
= 150
And
7(5) - 20
= 150
Now, we know that the sum of angle of triangle is 1800.
So,
Maths-General
Solution:
Hint:
We have a given figure

In this figure,

4x = 20
x = 50
So,

= 150
And

7(5) - 20
= 150
Now, we know that the sum of angle of triangle is 1800.
So,




Hint:
- the base angle theorem states that if the sides of a triangle are congruent then the angles opposite these sides are congruent.
- We have been given in the question diagram of a triangle named ABC where ∠ABC=60.
- We have to find out angle A.
We have a given figure
In this figure,
4x = 20
x = 50
So,
= 150
And
7(5) - 20
= 150
Now, we know that the sum of angle of triangle is 1800.
So,
Maths-
Use Symmetric Property of Equality: If x = y, then
Hint :- The symmetric property states that for any real numbers, a and b, if a = b then b = a.
Ans :- Option B
Explanation :- The symmetric property states that for any real numbers, a and b, if a = b then b = a.
Similarly with x and y If x = y, then y = x
∴ Option B
Ans :- Option B
Explanation :- The symmetric property states that for any real numbers, a and b, if a = b then b = a.
Similarly with x and y If x = y, then y = x
∴ Option B
Use Symmetric Property of Equality: If x = y, then
Maths-General
Hint :- The symmetric property states that for any real numbers, a and b, if a = b then b = a.
Ans :- Option B
Explanation :- The symmetric property states that for any real numbers, a and b, if a = b then b = a.
Similarly with x and y If x = y, then y = x
∴ Option B
Ans :- Option B
Explanation :- The symmetric property states that for any real numbers, a and b, if a = b then b = a.
Similarly with x and y If x = y, then y = x
∴ Option B
Maths-
If
and
, find the value of x and 

Solution:
Hint:
In the given figure,


So,


x = 9
So,

= 5(9) + 7
= 520
And,

= 2(9) + 34
= 520
Now we know that the sum of angle of triangle is 1800.
So,




Hint:
- the base angle theorem states that if the sides of a triangle are congruent then the angles opposite these sides are congruent.
- We have been given in the question that if 𝑚∠𝐵 = (5𝑥 + 7) ° and 𝑚∠𝐶 = (2𝑥 + 34) °
- We have to find the value of x and 𝑚∠A
In the given figure,
So,
x = 9
So,
= 5(9) + 7
= 520
And,
= 2(9) + 34
= 520
Now we know that the sum of angle of triangle is 1800.
So,
If
and
, find the value of x and 

Maths-General
Solution:
Hint:
In the given figure,


So,


x = 9
So,

= 5(9) + 7
= 520
And,

= 2(9) + 34
= 520
Now we know that the sum of angle of triangle is 1800.
So,




Hint:
- the base angle theorem states that if the sides of a triangle are congruent then the angles opposite these sides are congruent.
- We have been given in the question that if 𝑚∠𝐵 = (5𝑥 + 7) ° and 𝑚∠𝐶 = (2𝑥 + 34) °
- We have to find the value of x and 𝑚∠A
In the given figure,
So,
x = 9
So,
= 5(9) + 7
= 520
And,
= 2(9) + 34
= 520
Now we know that the sum of angle of triangle is 1800.
So,
Maths-
Use Substitution Property of Equality: If PQ = 10 cm , then PQ + RS =
Hint :- substitute the given value and choose the option .
Ans :- Option C
Explanation :-
If PQ = 10 cm
then PQ + RS = 10 cm + RS
∴ Option C
Ans :- Option C
Explanation :-
If PQ = 10 cm
then PQ + RS = 10 cm + RS
∴ Option C
Use Substitution Property of Equality: If PQ = 10 cm , then PQ + RS =
Maths-General
Hint :- substitute the given value and choose the option .
Ans :- Option C
Explanation :-
If PQ = 10 cm
then PQ + RS = 10 cm + RS
∴ Option C
Ans :- Option C
Explanation :-
If PQ = 10 cm
then PQ + RS = 10 cm + RS
∴ Option C
Maths-
Find the length of each side of the given regular dodecagon.

Solution:
Hint:
We have given a regular dodecagon with sides represented as
Since, It is regular, then all sides are equal
So,

2x - 1 = 9x + 15
7x = - 16
X can not be negative
Wrong data
Hint:
- A regular dodecagon has 12 sides equal in length and all the angles have equal measures, all the 12 vertices are equidistant from the center of dodecagon.
- A regular dodecagon is a symmetrical polygon.
- We have been given in the question figure of a regular dodecagon
- We have also been given the two sides of it that is -
- We have to find length of each side of the regular dodecagon.
We have given a regular dodecagon with sides represented as
Since, It is regular, then all sides are equal
So,
2x - 1 = 9x + 15
7x = - 16
X can not be negative
Wrong data
Find the length of each side of the given regular dodecagon.

Maths-General
Solution:
Hint:
We have given a regular dodecagon with sides represented as
Since, It is regular, then all sides are equal
So,

2x - 1 = 9x + 15
7x = - 16
X can not be negative
Wrong data
Hint:
- A regular dodecagon has 12 sides equal in length and all the angles have equal measures, all the 12 vertices are equidistant from the center of dodecagon.
- A regular dodecagon is a symmetrical polygon.
- We have been given in the question figure of a regular dodecagon
- We have also been given the two sides of it that is -
- We have to find length of each side of the regular dodecagon.
We have given a regular dodecagon with sides represented as
Since, It is regular, then all sides are equal
So,
2x - 1 = 9x + 15
7x = - 16
X can not be negative
Wrong data
Maths-
Draw a quadrilateral that is not regular.
Solution:
Hint:
Hint:
- A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices, and four angles.
- We have been given information in the question to draw a quadrilateral that is not regular.
Draw a quadrilateral that is not regular.
Maths-General
Solution:
Hint:
Hint:
- A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices, and four angles.
- We have been given information in the question to draw a quadrilateral that is not regular.
Maths-
Which of the statements is TRUE?
Explanation:
Option A:
A semicircle is a polygon.
No this is not true, because polygon only contain straight lines.
Option B:
A concave polygon is regular
It is not necessary that a concave polygon is regular.
So, it is not true
Option C:
A regular polygon is equiangular
Yes this is true, a regular polygon is equiangular and equilateral.
Option D:
Every triangle is regular
This is not true, because mant triangles are not regulat.
Hence, Option C is correct.
- We have been given four statements in the question from which we have to choose which statement is true.
- In the given four statements we have been given information about the semicircle, concave polygon, triangle and regular polygon.
Option A:
A semicircle is a polygon.
No this is not true, because polygon only contain straight lines.
Option B:
A concave polygon is regular
It is not necessary that a concave polygon is regular.
So, it is not true
Option C:
A regular polygon is equiangular
Yes this is true, a regular polygon is equiangular and equilateral.
Option D:
Every triangle is regular
This is not true, because mant triangles are not regulat.
Hence, Option C is correct.
Which of the statements is TRUE?
Maths-General
Explanation:
Option A:
A semicircle is a polygon.
No this is not true, because polygon only contain straight lines.
Option B:
A concave polygon is regular
It is not necessary that a concave polygon is regular.
So, it is not true
Option C:
A regular polygon is equiangular
Yes this is true, a regular polygon is equiangular and equilateral.
Option D:
Every triangle is regular
This is not true, because mant triangles are not regulat.
Hence, Option C is correct.
- We have been given four statements in the question from which we have to choose which statement is true.
- In the given four statements we have been given information about the semicircle, concave polygon, triangle and regular polygon.
Option A:
A semicircle is a polygon.
No this is not true, because polygon only contain straight lines.
Option B:
A concave polygon is regular
It is not necessary that a concave polygon is regular.
So, it is not true
Option C:
A regular polygon is equiangular
Yes this is true, a regular polygon is equiangular and equilateral.
Option D:
Every triangle is regular
This is not true, because mant triangles are not regulat.
Hence, Option C is correct.
Maths-
The length of each side of a nonagon is 8 in. Find its perimeter
Solution:
Hint:
We have length of each side of a nanagon 8in
Now the perimeter will be
9 × 8in
72in
Hence, Option C is correct.
Hint:
- A nonagon is a polygon with nine sides and nine angles which can be regular, irregular, concave or convex depending upon its sides and interior angles.
- We have been given the length of each side of a nonagon that is 8 in.
- We have to find the perimeter of the given nonagon.
We have length of each side of a nanagon 8in
Now the perimeter will be
9 × 8in
72in
Hence, Option C is correct.
The length of each side of a nonagon is 8 in. Find its perimeter
Maths-General
Solution:
Hint:
We have length of each side of a nanagon 8in
Now the perimeter will be
9 × 8in
72in
Hence, Option C is correct.
Hint:
- A nonagon is a polygon with nine sides and nine angles which can be regular, irregular, concave or convex depending upon its sides and interior angles.
- We have been given the length of each side of a nonagon that is 8 in.
- We have to find the perimeter of the given nonagon.
We have length of each side of a nanagon 8in
Now the perimeter will be
9 × 8in
72in
Hence, Option C is correct.
Maths-
The lengths (in inches) of two sides of a regular pentagon are represented by the expressions 4x + 7 and x + 16. Find the length of a side of the pentagon.
Solution:
Hint:
The length of the two sides of a regular pentagon is represented by x + 16; 4x + 7
Now, We know that all sides of regular polygon are equal.
So,
X + 16 = 4x + 7
3x = 16 - 7
3x = 9
x = 3
And the measure of length will be
= x + 16
= 3 + 16
= 19
Hint:
- A regular pentagon is a polygon that has 5 sides all of same length and all the angles of the same measure.
- We have been given the two sides of a regular pentagon in the form of expressions that is -
- 4x + 7 and x + 16
- We have to find the length of a side of the pentagon.
The length of the two sides of a regular pentagon is represented by x + 16; 4x + 7
Now, We know that all sides of regular polygon are equal.
So,
X + 16 = 4x + 7
3x = 16 - 7
3x = 9
x = 3
And the measure of length will be
= x + 16
= 3 + 16
= 19
The lengths (in inches) of two sides of a regular pentagon are represented by the expressions 4x + 7 and x + 16. Find the length of a side of the pentagon.
Maths-General
Solution:
Hint:
The length of the two sides of a regular pentagon is represented by x + 16; 4x + 7
Now, We know that all sides of regular polygon are equal.
So,
X + 16 = 4x + 7
3x = 16 - 7
3x = 9
x = 3
And the measure of length will be
= x + 16
= 3 + 16
= 19
Hint:
- A regular pentagon is a polygon that has 5 sides all of same length and all the angles of the same measure.
- We have been given the two sides of a regular pentagon in the form of expressions that is -
- 4x + 7 and x + 16
- We have to find the length of a side of the pentagon.
The length of the two sides of a regular pentagon is represented by x + 16; 4x + 7
Now, We know that all sides of regular polygon are equal.
So,
X + 16 = 4x + 7
3x = 16 - 7
3x = 9
x = 3
And the measure of length will be
= x + 16
= 3 + 16
= 19
Maths-
Two angles of a regular polygon are given to be
Find the value of and measure of each angle.
Solution:
Hint:
We know that a regulat polygon is equiangular
So,
2x + 27 = 3x - 3
x = 27 + 3
x = 30
And the value of each angle will be
= 2x + 27
= 2(30) + 27
= 87
Hint:
- A polygon whose length of all sides is equal with equal angles at each vertex is called regular polygon.
- We have been given the two sides of a regular polygon that is - (2𝑥 + 27)° 𝑎𝑛𝑑 (3𝑥 − 3)°
- We have to find the value of x and measure of each angle.
We know that a regulat polygon is equiangular
So,
2x + 27 = 3x - 3
x = 27 + 3
x = 30
And the value of each angle will be
= 2x + 27
= 2(30) + 27
= 87
Two angles of a regular polygon are given to be
Find the value of and measure of each angle.
Maths-General
Solution:
Hint:
We know that a regulat polygon is equiangular
So,
2x + 27 = 3x - 3
x = 27 + 3
x = 30
And the value of each angle will be
= 2x + 27
= 2(30) + 27
= 87
Hint:
- A polygon whose length of all sides is equal with equal angles at each vertex is called regular polygon.
- We have been given the two sides of a regular polygon that is - (2𝑥 + 27)° 𝑎𝑛𝑑 (3𝑥 − 3)°
- We have to find the value of x and measure of each angle.
We know that a regulat polygon is equiangular
So,
2x + 27 = 3x - 3
x = 27 + 3
x = 30
And the value of each angle will be
= 2x + 27
= 2(30) + 27
= 87
Maths-
Solve the equation. Write a reason for each step.
8(−x − 6) = −50 − 10x
Hint :- using the additive property and subtraction property ,division property on both sides .solve for x.
Ans:- x = 1
Explanation :-
Given ,8(-x − 6) = -50-10x.
By left distributive property - 8x − 48 = - 50 -10x
Adding 48 on both sides by additive property of equality both sides remain equal.
- 8x − 48 + 48 = - 50 -10x + 48
- 8x = -10x - 2
Adding 10x on both sides by additive property of equality both sides remain equal.
- 8x +10x = -10x - 2 +10x
2x = - 2
Dividing 2
by division property of equality both sides remains equal.

x = -1
∴ x = -1
Ans:- x = 1
Explanation :-
Given ,8(-x − 6) = -50-10x.
By left distributive property - 8x − 48 = - 50 -10x
Adding 48 on both sides by additive property of equality both sides remain equal.
- 8x − 48 + 48 = - 50 -10x + 48
- 8x = -10x - 2
Adding 10x on both sides by additive property of equality both sides remain equal.
- 8x +10x = -10x - 2 +10x
2x = - 2
Dividing 2
x = -1
∴ x = -1
Solve the equation. Write a reason for each step.
8(−x − 6) = −50 − 10x
Maths-General
Hint :- using the additive property and subtraction property ,division property on both sides .solve for x.
Ans:- x = 1
Explanation :-
Given ,8(-x − 6) = -50-10x.
By left distributive property - 8x − 48 = - 50 -10x
Adding 48 on both sides by additive property of equality both sides remain equal.
- 8x − 48 + 48 = - 50 -10x + 48
- 8x = -10x - 2
Adding 10x on both sides by additive property of equality both sides remain equal.
- 8x +10x = -10x - 2 +10x
2x = - 2
Dividing 2
by division property of equality both sides remains equal.

x = -1
∴ x = -1
Ans:- x = 1
Explanation :-
Given ,8(-x − 6) = -50-10x.
By left distributive property - 8x − 48 = - 50 -10x
Adding 48 on both sides by additive property of equality both sides remain equal.
- 8x − 48 + 48 = - 50 -10x + 48
- 8x = -10x - 2
Adding 10x on both sides by additive property of equality both sides remain equal.
- 8x +10x = -10x - 2 +10x
2x = - 2
Dividing 2
x = -1
∴ x = -1
Maths-
Find the measure of each angle of an equilateral triangle using base angle theorem.
Solution:
Hint:
Let a triangle be ABC

Here,
AB = AC
Using base angle theorem

And,
So,
Therefore,

Step 2 of 2:
We know that the sum of all angles of a triangle is 1800.
Now,




So,

Hint:
- the base angle theorem states that if the sides of a triangle are congruent then the angles opposite these sides are congruent.
- An equilateral triangle is a triangle with all the three sides of equal length.
- We have to find the measure of each angle of an equilateral triangle using base angle theorem.
Let a triangle be ABC
Here,
AB = AC
Using base angle theorem
And,
So,
Therefore,
Step 2 of 2:
We know that the sum of all angles of a triangle is 1800.
Now,
So,
Find the measure of each angle of an equilateral triangle using base angle theorem.
Maths-General
Solution:
Hint:
Let a triangle be ABC

Here,
AB = AC
Using base angle theorem

And,
So,
Therefore,

Step 2 of 2:
We know that the sum of all angles of a triangle is 1800.
Now,




So,

Hint:
- the base angle theorem states that if the sides of a triangle are congruent then the angles opposite these sides are congruent.
- An equilateral triangle is a triangle with all the three sides of equal length.
- We have to find the measure of each angle of an equilateral triangle using base angle theorem.
Let a triangle be ABC
Here,
AB = AC
Using base angle theorem
And,
So,
Therefore,
Step 2 of 2:
We know that the sum of all angles of a triangle is 1800.
Now,
So,
Maths-
The length of each side of a regular pentagon is . Find the value of if its perimeter is .
Solution:
Hint:
We have given a perimeter of a regular pentaogn 50.
A pentagon has sides.
The length of the side is x+5
So,
5(x + 5) = 50
x + 5 = 10
x = 5
Hence, Option A is correct.
Hint:
- A regular pentagon is a polygon that has 5 sides all of same length and all the angles of the same measure.
- We have been given in the question the length of each side of a regular pentagon which is (x+5) cm
- We have also been given the perimeter that is 50 cm.
- We have to find the value of x.
We have given a perimeter of a regular pentaogn 50.
A pentagon has sides.
The length of the side is x+5
So,
5(x + 5) = 50
x + 5 = 10
x = 5
Hence, Option A is correct.
The length of each side of a regular pentagon is . Find the value of if its perimeter is .
Maths-General
Solution:
Hint:
We have given a perimeter of a regular pentaogn 50.
A pentagon has sides.
The length of the side is x+5
So,
5(x + 5) = 50
x + 5 = 10
x = 5
Hence, Option A is correct.
Hint:
- A regular pentagon is a polygon that has 5 sides all of same length and all the angles of the same measure.
- We have been given in the question the length of each side of a regular pentagon which is (x+5) cm
- We have also been given the perimeter that is 50 cm.
- We have to find the value of x.
We have given a perimeter of a regular pentaogn 50.
A pentagon has sides.
The length of the side is x+5
So,
5(x + 5) = 50
x + 5 = 10
x = 5
Hence, Option A is correct.
Maths-
Name the property of equality the statement illustrates.
Every segment is congruent to itself.
Hint :- The reflexive property states that any real number, a, is equal to itself i.e a = a.
Ans :- Option A
Explanation :-
The reflexive property states that any real number, a, is equal to itself. That is, a = a.
Similarly the segment is congruent to itself .
∴Option A
Ans :- Option A
Explanation :-
The reflexive property states that any real number, a, is equal to itself. That is, a = a.
Similarly the segment is congruent to itself .
∴Option A
Name the property of equality the statement illustrates.
Every segment is congruent to itself.
Maths-General
Hint :- The reflexive property states that any real number, a, is equal to itself i.e a = a.
Ans :- Option A
Explanation :-
The reflexive property states that any real number, a, is equal to itself. That is, a = a.
Similarly the segment is congruent to itself .
∴Option A
Ans :- Option A
Explanation :-
The reflexive property states that any real number, a, is equal to itself. That is, a = a.
Similarly the segment is congruent to itself .
∴Option A
Maths-
Solution:
Hint:
We have given figure

Here, AB = AC
It means the given triangle is an isosceles triangle.
Now,
By base angle theorem
.
And it is given
So,
Step 2 of 2:
We know that the sum of angle of a triangle is 1800





Hint:
- the base angle theorem states that if the sides of a triangle are congruent then the angles opposite these sides are congruent.
- We have been given a diagram of a triangle in the question named ABC we have also been given 𝑚∠𝐵 = 55°.
- We have to find out 𝑚∠A.
We have given figure
Here, AB = AC
It means the given triangle is an isosceles triangle.
Now,
By base angle theorem
And it is given
So,
Step 2 of 2:
We know that the sum of angle of a triangle is 1800
Maths-General
Solution:
Hint:
We have given figure

Here, AB = AC
It means the given triangle is an isosceles triangle.
Now,
By base angle theorem
.
And it is given
So,
Step 2 of 2:
We know that the sum of angle of a triangle is 1800





Hint:
- the base angle theorem states that if the sides of a triangle are congruent then the angles opposite these sides are congruent.
- We have been given a diagram of a triangle in the question named ABC we have also been given 𝑚∠𝐵 = 55°.
- We have to find out 𝑚∠A.
We have given figure
Here, AB = AC
It means the given triangle is an isosceles triangle.
Now,
By base angle theorem
And it is given
So,
Step 2 of 2:
We know that the sum of angle of a triangle is 1800