Question

How do you factor 35x^2+26-16? Show work please.

Answer 1

well, first off, we do a quick prime factoring of the leading term's coefficient, 35, and the constant, 16.

35 = 5*7

16 = 2*2*2*2

and the rest is just a mix and match.

what combination from the factors of 35 and the factors of 16, can provide a product whose sum is the middle term 26?  well, without further adieu.

we can try 5*2*2  + 7*2*2, and that's 20 and 28, ok, 28 - 20 is 8, so that won't work.

another can be 5*2*7  and 2*2, that's 70 and 4, 70 - 4 is 56, that won't work either.

5*2*2*2 and 7*2, that's 40 and 14, hmmm 40 - 14 = 26!!! holly guacamole!

so then,

$\bf 35x^2+26x-16\implies (5x-\stackrel{\stackrel{2}{\downarrow }}{2})(7x+\stackrel{\stackrel{2\cdot 2\cdot 2}{\downarrow }}{8})$