Algebra II help?

Question

These two problems have to do with factoring polynomials by grouping...how do I do this? I need steps, not just the answer.

1. 10x^3 + 20x^2 + x +2
2. 2x^3 - x^2 + 2x -1

Thanks!

Answer 1

You really should be trying to solve this on your own, but maybe you're just begining, so you may need some help...Okay lets see..
1. 10x^3+20x^2+x+2 or 10x*x^2+2*10x^2+x+2
or 10x^2*x+10x^2*2+x+2 (I just rearranged stuff)
or 10x^2(x+2)+(x+2) or (x+2)(10x^2+1)

2. 2x^3-x^2+2x-1 or 2x*x^2-x^2+2x-1
or (rearranging) x^2(2x-1)+(2x-1) or (2x-1)(x^2+1)

If you notice how I tackle the problems, you'll see that I start by first trying to see what is the highest common factor between adjacent terms. I factor them out and keep the rest of the terms in a bracket. The terms in the bracket are like numbers themselves, so if you find some that are common, you can lump them together. Keep repeating this process if you have a higher order algebraic expression (eg. x^12 etc). Soon you'll be able to pair things off and arrive at the factorized form. Hope that helps!

Answer 2

There iis no simple formula for factoring cubics.
What you do is guess a factor and try it out

(1) The possibilities come from

plus or minus[ (the factors of 2) / (the factors of 10) ]

This can be really tedious and messy so try easy ones but note for this cubic if (x + A) is a factor then A must be positive

Try ( x + 1), (x + 2), to start with using synthetic division or the remainder theorem.

Here you get (x + 2) as a factor and dividing it out leaves a quadratic

Answer 3

10x^3 + 20x^2 + x +2
10x^3 + x +2+ 20x^2
x(10x^2+1)+2(1+10x^2)
(10x^2+1)(x+2)


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

Answer 4

1. 10x^3 + 20x^2 + x +2
=10x^2(x+2) + x+2
= (10x^2+1)(x+2)

2. 2x^3 - x^2 + 2x -1
=x^2(2x-1) +2x-1
=( x^2+1)(2x-1)

Answer 5

10x^2(x+2) + (x+2) = (10x^2+1)(x+2)

x^2(2x-1) + (2x-1) = (x^2+1)(2x-1)

Answer 6

I stink at factoring but I would try going to coolmath.com they have all sorts of help with this! Sorry I couldn't be more help. Good luck! Try coolmath.com I have had alot of success so have others I know with this web site.