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 [math]a^2+ b^2[/math] 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.