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Factoring Review

Math 10. Factoring Review. Types of Factoring. Greatest Common Factor (GCF) Trinomial without a leading coefficient ( x 2 + bx + c) Trinomial with a leading coefficient ( ax 2 + bx + c) Difference of Squares (x 2 - y 2 ). 1) Greatest Common Factor. Factor. Solution:.

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Factoring Review

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  1. Math 10 Factoring Review

  2. Types of Factoring • Greatest Common Factor (GCF) • Trinomial without a leading coefficient ( x2 + bx + c) • Trinomial with a leading coefficient ( ax2 + bx + c) • Difference of Squares (x2 - y2)

  3. 1) Greatest Common Factor Factor Solution: *To find GCF: - take GCF of the coefficients - for each variable, use the LOWEST exponent GCF = ) ( *To determine what is left inside the brackets: - take each term and divide by the GCF

  4. 2) Factoring x2+bx+c Factor *Notice that there is a coefficient of 1 in front of the x2 Solution: *Find two numbers that: • - multiply to the last term • - Adds to the middle coefficient

  5. 3) Factoring ax2+bx+c Factor • *Notice that the coefficient in front of the x2 is NOT 1 *Need to use DECOMPOSITION.

  6. Factor 3x2-19x+20 • Multiply first and last coefficients together. • Find two numbers that multiplies to your answer in step 1 but adds to the middle coefficient.

  7. Factor 3x2-19x+20 • Use the two numbers from step 2 to split the middle term. • Group the first two terms and the last two terms together. Then factor out the GCF from each group.

  8. Factor 3x2-19x+20 • The GCFs will form one factor, while the binomial will form the other factor.

  9. You Try! Factor the following: 1) 2) 3)

  10. Answers: 1) Solution: GCF = ) (

  11. Answers: 2) Solution:

  12. Answers: 3)

  13. Combination Problems • Always look for a GCF first and factor it out if there is one. • Then determine if you can factor what is left.

  14. Ex. Factor 18X3+21X2+6X GCF =

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