Factoring Polynomials Tutorial & Examples
Learn how to factor polynomials with this comprehensive tutorial covering factoring using GCF, sum/difference of cubes, factor by grouping, and more. Practice examples provided to improve your understanding of polynomial factoring techniques.
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Presentation Transcript
4.4 Notes: Factoring Polynomials
Factoring using a GCF: We can start by trying to pull out a GCF. Remember, there WILL be more factoring to do after this! A) x3 4x2 5x B) 3y5 48y3 C) 5z4+ 30z345z2
Factoring sum or difference of cubes: Sum or difference of cubes has: oOnly two terms oTwo perfect cubes You need to use one of these two formulas to factor sum or difference of cubes no other factoring method works! SUM: (a + b)(a2 ab + b2) DIFFERENCE: (a b)(a2+ ab + b2)
SUM: (a + b)(a2ab + b2) DIFFERENCE: (a b)(a2+ ab + b2) 1) look for GCF 2) make in to perfect cubes to use the formulas above A) x3 125 B) 27x3 8 C) 64x3+ 1
Factor by Grouping: This method is part of the factoring of quadratics method that we have been using. A) z3+ 5z2 4z 20 B) 3y3+ y2+ 9y + 3 C) x3+ 2x2 9x + 18
A divisor is a factor of a polynomial is the remainder is zero
Finally.. Show that x + 3 is a factor of f(x) = x4 + 3x3 x 3, then factor completely. Step 1: use synthetic division to determine if x+3 is a factor Step 2: factor the polynomial.
And. Show that x 2 is a factor of f(x) = x4 2x3 + x 2 then factor completely.
