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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;

1- When these are added

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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