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:

`((2)/(2))(2x^2+13x-7)=(4x^2+26x-14)/(2)`

which we can write in the following way:

`(4x^2+26x-14)/(2)=((2x)^2+13(2x)-14)/(2)`

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

`((2x)^2+13(2x)-14)/(2)=((2x-1)(2x+14))/(2)`

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

`((2x-1)(2x+14))/(2)=((2x-1)(x+7)(2))/(2)=(2x-1)(x+7)`

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