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**PATTERNS, ALGEBRA, AND FUNCTIONS**

AIMS TARGET PATTERNS, ALGEBRA, AND FUNCTIONS

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**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.

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

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**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)

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Try this!! Factor 20x2y – 45xy2

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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.

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

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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)

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

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**Completely factoring polynomials**

Try these!! Factor 2x4 – 4x3 – 70x2 Factor 16x4 - 81

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