Question 4: Factorize 30 x 2 + 7 x − 15

Question 4: Factorize 30 x 2 + 7 x − 15

Factorization exercises , factorization examples

Solution :

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

$30x^2+7x-15$

If we multiply last term i-e (-15) with the first term ​i-e $$30x^2$$​ we get ​$$-450x^2$$​. So we make break mid term i-e 7x into two parts such that if we add these two parts then we get 7x — and if we multiply these two parts we get  ​$$-450x^2$$

We can think of -25x and 18x because

1- when added together i-e (-25x)+18x = -25x+18x= 7x

2- when multiplied together i-e (-25x)(18x) = ​$$-450x^2$$

So we can write;

$=30x^2-25x+18x-15$

taking 5x as common from first two terms and 3 as common from last two terms – we get;

$\[ = 5x(6x-5)+3(6x-5)$ \]

or

$= [5x(6x-5)+3(6x-5) ]$

Taking (6x-5) as common from the whole expression – we get;

$=(5x+3)[6x-5]$

or

$=(5x+3)(6x-5)$

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