Question

# What must be added to 5y^{2}+3y + 1 to get 3y^{3} -7y^{2}+8

Hint:

### Addition of polynomials.

○ Always take like terms together while performing addition.

○ In addition to polynomials only terms with the same coefficient are added.

## The correct answer is: Hence, the other term must add is 3y3 - 12y2 - 3y + 7.

### Answer:

- Step by step explanation:

○ Given:

Terms:

5y^{2}+3y + 1

3y^{3} -7y^{2}+8

○ Step 1:

○ Let A must be added to 5y^{2}+3y + 1 to get 3y^{3} -7y^{2}+8.

So,

A + 5y^{2}+ 3y + 1 =3y^{3} -7y^{2}+8

A = (3y^{3} -7y^{2}+8) - (5y^{2 }+ 3y + 1)

A = 3y^{3} - 7y^{2 }+ 8 - 5y^{2 }- 3y - 1

A = 3y^{3} - 7y^{2 }- 5y^{2 }- 3y + 8 - 1

A = 3y^{3} - 12y^{2 }- 3y + 7

- Final Answer:

Hence, the other term must add is 3y^{3} - 12y^{2 }- 3y + 7.

^{2}+3y + 1

^{3}-7y

^{2}+8

○ Step 1:

○ Let A must be added to 5y

^{2}+3y + 1 to get 3y

^{3}-7y

^{2}+8.

So,

^{2}+ 3y + 1 =3y

^{3}-7y

^{2}+8

^{3}-7y

^{2}+8) - (5y

^{2 }+ 3y + 1)

^{3}- 7y

^{2 }+ 8 - 5y

^{2 }- 3y - 1

^{3}- 7y

^{2 }- 5y

^{2 }- 3y + 8 - 1

^{3}- 12y

^{2 }- 3y + 7

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¶The standard form of a linear equation in one variable is: ax + b = 0

Where,

The letters 'a' and 'b' are real numbers.

'a' and 'b' are both greater than zero.

### In an academic contest correct answers earn 12 points and incorrect answers lose 5

points. In the final round, school A starts with 165 points and gives the same number

of correct and incorrect answers. School B starts with 65 points and gives no incorrect answers and the same number of correct answers as school A. The game ends with the two schools tied.

ii)How many answers did each school get correct in the final round?

A linear equation in one variable is an equation that has only one solution and is expressed in the form ax+b = 0, where a and b are two integers and x is a variable. 2x+3=8, for example, is a linear equation with a single variable. As a result, this equation has only one solution, x = 5/2.

¶The standard form of a linear equation in one variable is: ax + b = 0

Where,

The letters 'a' and 'b' are real numbers.

'a' and 'b' are both greater than zero.