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