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)#