How do you factor completely $2x^2 + 2x -40$ ?

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Answer 1 · 2016-05-24T13:19:16

$2x^2+2x-40=2(x-4)(x+5)$

To factorize a quadratic polynomial of type $ax^2+bx+c$ ,

one needs to split middle term $b$ in two parts whose product is $ac$ . As in $2x^2+2x-40$ , the product is $-80$ , these are $10$ and $-8$ .

Hence, $2x^2+2x-40$

= $2x^2+10x-8x-40$

= $2x(x+5)-8(x+5)$

= $(2x-8)(x+5)$

= $2(x-4)(x+5)$

How do you factor completely 2x^2 + 2x -402x^2 + 2x -40?