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Thread: Factoring Polynomials

  1. #1

    Unhappy Factoring Polynomials

    I don't understand factoring - here are some problewms I am looking to see complete step by step because no matter what I do I am not getting the right answers!!

    6x^2y^2 + 12xy^2 + 12y^2

    a^2 + 2a - 24

    z^3 + 9z^2 +18z

    a^4 - ab3

    and then for review I am confused on these:
    t^8 / t^2


    I have read the book and gone step by step but something just isn't clicking... I am desperate as I have a test next week and I can't even do my homework!
    Thank you in advance to anyone who helps!
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  2. #2
    Junior Member
    Jun 2007
    Ok let's start off with one. Notice anything similar with the 3 terms? They all have $\displaystyle 6y^{2}$ in them so we can factor out $\displaystyle 6y^{2} $ and get $\displaystyle 6y^{2}(x^{2} + 2x + 2) $ I don't think that can be factored any further. Well without getting into complex roots.

    Now #2-
    Let's find factors of -24 that will give us 2. about 6 and -4? That will give us $\displaystyle (x+6)(x-4)$ Expand and check your work if you need to.

    #3- Hmm notice something in these three terms too? Yup z is in all 3 so take that out of there $\displaystyle z(z^{2}+9z+18)$ Now let's find factors of 18 that will sum to 9. Aha! 6 & 3 So that gives us $\displaystyle (x+6)(x+3)$ Expand and check if needed.

    #4- Hmmm...there's an a in both terms there so get him out of there. $\displaystyle a(a^{3} - b^{3})$ Now we're going to factor out cubes (I don't know if you guys are doing this yet, but I'll show you anyway, sorry if this confuses you) We'll take the cubed root of a and b and get $\displaystyle (a-b)$ then we square the first term multiply the 1st and 2nd term once and switch the sign and then square the last term to get $\displaystyle a(a-b)(a^{2}+ab+b^{2})$ and we have factored the polynomial.

    For the last to just simplify $\displaystyle \frac{a^{5}}{a^{3}} = a^{5-3}$ apply that do both of those. (Don't forget to simplify $\displaystyle \frac{8}{2}$ as well.)
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