Mastering Factoring Polynomials: Tips, Tricks, and Examples to Help You Succeed!

[CamTheLamb]

Alright, I'll be honest. I was extremely tired and slept all through the lesson in Algebra today lol.
And now I need help with factoring polynomials.

Example problems that I need help on:
7h³+448
Perfect square factoring - y⁴-81
Grouping - 3n³-10n²-48n+160

You don't have to answer those problems (Though it would help =P), I just need a quick lesson or the formula for factoring these.
Thanks =)

 

[magwas]

http://www.jamesbrennan.org/algebra/polynomials/factoring_polynomials.htm

 

[HallsofIvy]

Alright, I'll be honest. I was extremely tired and slept all through the lesson in Algebra today lol.
And now I need help with factoring polynomials.

Example problems that I need help on:
7h³+448

The first thing I would do is try to factor out a 7: $7(h^3- 64)$ which is wonderful because it is now $7(x^3- 4^3)$.
You need to know that $a^2- b^3= (a- b)(a^2+ ab+ b^2)$

Perfect square factoring - y⁴-81

Yes, those are perfect squares: $(y^2)^2- 9^2$ and, of course, $a^2- b^2= (a-b)(a+b)$. After you have used that you will still have a "difference of squares" in one factor and can use that again. There is no way to factor \(\displaystyle a^2+ b^2\) with real coefficients.

Grouping - 3n³-10n²-48n+160

Well, 10 isn't divisible by 3 but 48 is so I would try $3n^3- 48n= 3n(n^2- 16)$. Aha! Now it's easy to see that $-10n^2+ 160= -10(n^2- 16)$

$3n^3- 10n- 48n+ 160= 3n(n^2- 16)- 10(n^2- 16)$
That isn't the answer- you need to finish it.

You don't have to answer those problems (Though it would help =P), I just need a quick lesson or the formula for factoring these.
Thanks =)

 

[CamTheLamb]

Thanks for the help, I knew it was something similar to this, just didn't know any formulas.