# Factorize Each of the Following Algebraic Expression: 40 + 3x − X2 - Mathematics

Sum

Factorize each of the following algebraic expression:
40 + 3x − x2

#### Solution

We have:
$40 + 3x - x^2$
$\Rightarrow - ( x^2 - 3x - 40)$
$\text{ To factorise }( x^2 - 3x - 40),\text{ we will find two numbers p and q such that }p + q = - 3\text{ and pq }= - 40 .$
Now,
$5 + ( - 8) = - 3$
and
$5 \times ( - 8) = - 40$
$\text{ Splitting the middle term }- 3x \text{ in the given quadratic as }5x - 8x,\text{ we get: }$
$40 + 3x - x^2 = - ( x^2 - 3x - 40)$
$= - ( x^2 + 5x - 8x - 40)$
$= - [( x^2 + 5x) - (8x + 40)]$
$= - [x(x + 5) - 8(x + 5)]$
$= - (x - 8)(x + 5)$
$= (x + 5)( - x + 8)$

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#### APPEARS IN

RD Sharma Class 8 Maths
Chapter 7 Factorization
Exercise 7.7 | Q 2 | Page 27