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DanPatrick10 · Jan 18, 2009, 12:28 AM

I understand the idea of factoring by grouping for the most part, but some of the answers in the back of the book are baffling me.

Ex) 6x3 + 9x2 - 2x2 - 3x
=(6x3 + 9x2) - (2x2 - 3x)
=3x2(2x + 3) - 1(2x + 3)
My answer: (2x + 3)(3x - 1)
Book answer: x(2x + 3)(3x - 1)

galactus · Jan 18, 2009, 10:55 AM

First of all, use ^ to represent powers.

$6x^{3}+9x^{2}-2x^{2}-3x=6x^{3}+7x^{2}-3x$

Factor out an x:

$x(6x^{2}+7x-3)$

Now, there is a quadratic to deal with.

What two numbers when multiplied equal -18 and when added equal 7.

How about 9 and -2.

$x(6x^{2}+\underbrace{9x-2x}_{\text{7x}}-3)$

$x((6x^{2}+9x)-(2x+3))$

$x(3x(2x+3)-(2x+3))$

See? What's in the parnetheses is the same. That is crucial.

$x(3x-1)(2x+3)$

DanPatrick10 · Jan 18, 2009, 02:11 PM

According to the way you've done it, it looks like it leads into the next chapter.

princess94 · Mar 7, 2010, 06:09 PM

how do you factor by grouping 6v^3-16v^2+21v-56?

princess94 · Mar 7, 2010, 06:13 PM

how do you factor by grouping 6v^3-16v^2+21v-56?

Unknown008 · Mar 8, 2010, 06:52 AM

Don't post your question at several places please:

https://www.askmehelpdesk.com/high-s...-a-455502.html