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Mastering Polynomials: GCF, Factoring, and Binomials

Learn how to find the Greatest Common Factor, factor polynomials, and factor trinomials and binomials efficiently. Practice examples included.

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Mastering Polynomials: GCF, Factoring, and Binomials

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  1. AIMS TARGET PATTERNS, ALGEBRA, AND FUNCTIONS

  2. Finding the Greatest Common Factor (GCF) • Find the GCF of the coefficients of each monomial. • Find the variable(s) that are common to each monomial. • If there are any variables that are common, use the smallest exponent that the variable is raised to in the monomials.

  3. Try this!! • Find the GCF of 15x2y and 20xy

  4. Factoring the GCF from a polynomial • Find the GCF, and write it on the outside of a set of parenthesis. GCF( ) • Divide each term by the GCF, and write the result inside the parenthesis. • Example: • Factor 3x2 + 6x – 9 • 3(x2 + 2x – 3)

  5. Try this!! • Factor 20x2y – 45xy2

  6. Factoring trinomials • The discriminant is b2 – 4ac, and must be a “perfect square number” in order to factor a trinomial. Otherwise, it cannot be factored. • Steps to factor a trinomial: • (1) Determine first if b2 – 4ac is a perfect square. • (2) Find the product of a and |c|. • (3) Find two numbers whose product is the same as the product from Step 2 (above) and whose sum or difference is |b|, depending on whether c is positive (sum) or negative (difference). • (4) Rewrite the middle term of the trinomial as two terms using the factor pair from Step 2 as the coefficients. • (5) Group the first two terms and the last two terms of the new polynomial from Step 3 and factor the GCF from each. • (6) Write your answer as the product of the common binomial and the binomial formed by the GCFs from Step 4.

  7. Try this!! • Factor 8x2 – 19x + 6 • Factor 5x2 – 23x - 10

  8. Factoring binomials • Binomials in the form m2 – n2 are called the “difference of two squares.” To factor a binomial in this form, follow this formula: m2 – n2 = (m + n)(m – n)

  9. Try this!! • Factor x2 – 25 • Factor 9x2 – 49y4

  10. Completely factoring polynomials • Try these!! • Factor 2x4 – 4x3 – 70x2 • Factor 16x4 - 81

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