# Question 1: Factorize 9 x 2 + 21 x − 8

Question 1: Factorize 9 x 2 + 21 x − 8

Factorization exercises — Factorization examples

Solution:

To see as how to evaluate an expression for factorization, we write it

$9x^2+21x-8$

In this expression we multiply third i-e the last term  with the co-efficient of ​$$x^2$$​ i-e we multiply (-8) with (9) – in this way we get -72. Now we break co-efficient of x i-e 21 into two parts such that if parts are added we get 24 and if the parts are multiplied we get -72.

Here we can think of 24 and (-3) because;

i-e 24+(-3) = 24-3 = 21

2- When these are multiplied

i-e (24)(-3) = -72

$= 9x^2+24x-3x-8$

Taking 3x common from first two terms and -1 common from last two terms — we get;

$=3x(3x+8)-(3x+8)$

or

$=[3x(3x-8)-(3x-8)]$

Now (3x-8) can be taken out as common;

$=(3x-8)[3x-1]$

or

$=(3x-8)(3x-1)$

or

$=(3x-1)(3x+8)$

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