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Need a review on how to factor cubic polynomials

  • #1
So long story short, I have a friend who wants me to help her learn how to factor cubic polynomials. Normally I would just fess up and say I don't remember but it's something I'd like to review myself and lessons online aren't the clearest.

Here's one of the questions:

2x3+3x2-8x+3

I need a quick 101. Any help would be much appreciated!
 

Answers and Replies

  • #2
gb7nash
Homework Helper
805
1
So long story short, I have a friend who wants me to help her learn how to factor cubic polynomials. Normally I would just fess up and say I don't remember but it's something I'd like to review myself and lessons online aren't the clearest.

Here's one of the questions:

2x3+3x2-8x+3

I need a quick 101. Any help would be much appreciated!
Let's call your cubic polynomial f(x). You could use the rational roots test to help you find roots of the polynomial. Once you have a root (call it r), use long division: f(x)/(x-r). This should give you a quadratic, and to find the other two roots(call them s and t) just use the quadratic formula. So in the end, you'll get f(x) = 2(x-r)(x-s)(x-t).

If the rational root test fails, use http://planetmath.org/encyclopedia/CubicFormula.html [Broken] to find your roots. Note that you must factor out a 2 out of the whole expression before you can use these formulas.
 
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  • #3
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