The expression $16 x^{2} - 106 x - 105$ $16x^2-106x-105$ can be written as $(8 x + a) (2 x + b)$ $(8x + a)(2x + b)$ , where $a$ $a$ and $b$ $b$ are integers. What is $a + 2 b$ $a + 2b$ ?

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Question from AoPS. Please help!
I tried to do it and figured out that a+4b=-53 but...
yeah. anyways.

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Answer 1 · 2018-06-04T21:13:41

-23

If you factorise it (or you could use the formula) you get

$(8 x + 7) (2 x - 15)$ $(8x+7)(2x-15)$

This gives a=7 and b=-15
a+2b=7-30=-23