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Comprehensive Review of Factoring Techniques in Algebra

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This guide covers essential types of factoring in algebra, including the Greatest Common Factor (GCF), trinomials with and without a leading coefficient, and the difference of squares. You will learn step-by-step how to find the GCF of coefficients and variables, factor trinomials by identifying pairs of numbers that multiply and add to specific terms, and apply decomposition techniques for more complex equations. Engage with practice problems and solutions to reinforce your understanding of these critical algebraic concepts.

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Comprehensive Review of Factoring Techniques in Algebra

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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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