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)

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)

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

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

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

Don't post your question at several places please:

https://www.askmehelpdesk.com/high-school/how-do-you-factor-grouping-6v-3-16v-2-21v-56-a-455502.html