Question

Factor 2x^2 + 13x - 7

Answer 1

Given the expression:

$2x^2+13x-7$

if we multiply it by 2/2, we get the following:

$(\frac{2}{2})(2x^2+13x-7)=\frac{4x^2+26x-14}{2}$

which we can write in the following way:

$\frac{4x^2+26x-14}{2}=\frac{(2x)^2+13(2x)-14}{2}$

then, we can factor the numerator using 2x as a variable. Then, we have the following:

$\frac{(2x)^2+13(2x)-14}{2}=\frac{(2x-1)(2x+14)}{2}$

since the right factor has coefficients that are multiples of 2, we have:

$\frac{(2x-1)(2x+14)}{2}=\frac{(2x-1)(x+7)(2)}{2}=(2x-1)(x+7)$

therefore, the final factorization is (2x-1)(x+7)