FACTORING BINOMIALS.

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Factoring Polynomials.

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Presentation transcript:

FACTORING BINOMIALS

Factoring Binomials (4 Possibilities) • GCF (Greatest Common Factor) • Difference of Squares •Sum or Difference of Cubes • Prime (Not Factorable)

If a GCF exists, simply factor it out.

2nd Possibility DIFFERENCE OF 2 SQUARES If both terms in the binomial are squares and they are subtracted, a Simple Formula will give you the answer.

Example 1) The Difference of Squares Formula is Find a and b, then plug them into the formula.

Examples of Diff. Of Squares

Recognizing Monomial Squares Numbers that are perfect squares are: 1, 4, 9, 16, 25, 36… Variables that are perfect squares are: (Any even powered variable is a perfect square) Monomials that are perfect squares are: 2x2 Check this picture out. It shows why any even powered Variable is a perfect square. 2x2 4x4

Try These

3nd Possibility SUM or DIFFERENCE OF 2 CUBES If both binomials are cubes and they are added

If both binomials are cubes and they are subtracted To solve sum and difference of two cubes, simply solve for a and b. Then plug into the correct formula.

a b a = 3x b = 5 GCF FIRST! a = x b = 4 1. Factor completely

4th and last possibility when trying to factor a binomial If the binomial does not have a GCF & is not a Diff. Of Squares , Diff. of Cubes, or Sum of Cubes PRIME & NOT FACTORABLE

Examples of Prime Binomials

Which binomials are Prime?