Factoring 4x^2 + 31x - 8: how?

[calligrapher]

How do you factor 4x^2 + 31x - 8?

 

[soroban]

Re: Factoring?

How do you factor 4x^2 + 31x - 8?

$\displaystyle (4x\,-\,1)(x\,+\,8)$

 

[stapel]

How do you factor 4x^2 + 31x - 8?

You've been given the answer to this exercise, but of course that doesn't answer your question. Sorry 'bout that. :?

To learn the "how", try studying from online lessons:

. . . . .Google results for "factoring quadratics"

Note: Many lessons on this topic are divided up into the "easy" case, where the leading coefficient is "1" (or "where a = 1"), and the more difficult case, where the leading coefficient is not 1. You're looking for information on the harder case, but only start there if you're fine with the easy case, because the hard stuff relies on the easy stuff. :wink:

Have fun!

Eliz.

 

[jwpaine]

Factor by grouping

4x^2 + 31x - 8

4(8) = 32

what two factors of 32, when added, equal 31?

How about 32 and -1?

4x^2 + 32x - x - 8

group

(4x^2 + 32x) - (x - 8)

factor

4x(x + 8) -1(x + 8)

factor

(x+8)(4x - 1)