Mathematics

Grade10

Easy

Question

# Factorize the trinomial 6x^{2} + 7x – 3 as (px + q)(sx + t), where p, q, s and t are integers?

Hint:

### Algebraic expressions are those that are modelled utilising unknowable constants, coefficients, and variables. A constant has a fixed value, whereas a variable can have any value since it is not fixed. An algebraic expression with three terms is called a trinomial. Here we have given the trinomial 6x2 + 7x – 3 and we have to factories it as (px + q)(sx + t), where p, q, s and t are integers.

## The correct answer is:

### Now we know that an algebraic expression known as a trinomial has three non-zero terms and more than one variable. An example of a trinomial is a polynomial having three terms. It is in the form of ax^{2}+bx+c, for example: 5x^{4} - 4x^{2} +1.

Here we have given the term as 6x^{2} + 7x – 3.

We have:

a = 6

b = 7

c = -3

Now we will use middle term splitting method to factorise this expression, we get:

$= 6x+9x−2x−3$

$Now taking terms common, we get:$

$= 3x(2x+3) − (2x +3)$

$= (3x - 1)(2x + 3)$

$So here the factorisation is as (3x - 1)(2x + 3) in the form of (px + q)(sx + t)$

Here we used the concept of algebriac equations, trinomials and middle term splitting to factories the given expression. An expression with variables, constants, and algebraic operations is known as an algebraic expression (like subtraction, addition, multiplication, etc.). Terms comprise expressions. So the factorisation of 6x^{2} + 7x – 3 is (3x - 1)(2x + 3).