Factoring Polynomials. 1.Check for GCF 2.Find the GCF of all terms 3.Divide each term by GCF 4.The GCF out front 5.Remainder in parentheses Greatest Common.

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Factoring Polynomials.

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Presentation transcript:

Factoring Polynomials

1.Check for GCF 2.Find the GCF of all terms 3.Divide each term by GCF 4.The GCF out front 5.Remainder in parentheses Greatest Common Factor

Factor each polynomial completely.

Both terms are perfect squares The operation is subtraction The terms in each binomial are the square root of the terms in the problem One binomial is addition and one binomial is subtraction Difference of 2 Squares a² – b² = (a + b)(a – b)

Factor each polynomial completely.

Sum / Difference 2 Cubes a³ – b³ = (a – b)(a² + ab + b²) a³ + b³ = (a + b)(a² – ab + b²) Both terms are perfect cubes The operation may be addition or subtraction The terms are a binomial and a trinomial

The terms in the binomial are the cube roots of the terms in the problem with the same operation as the problem. The 1 st term in the trinomial is the square of the 1 st term in the binomial. The 2 nd term is the opposite of the product of the terms in the binomial. The 3 rd term is the square of the 2 nd term in the binomial.

Factor each polynomial completely.

1 st and 3 rd terms are perfect squares The middle term is twice the product of the square roots of the perfect square terms Perfect Square Trinomials a² + 2ab + b² = (a + b) ² a² – 2ab + b² = (a – b) ²

The terms in the binomial are the square roots of the perfect square terms in the problem The operation is the same as the middle term Perfect Square Trinomials

Factor each polynomial completely.

Trinomials Reverse FOIL Trinomial with a leading coefficient and / or a constant term that is prime. The first terms of the binomials are factors of the leading coefficient and the square roots of the variable factor. List the factors of the constant term and determine the combination that will add up to the middle term.

Factor each polynomial completely.

1.Multiply the leading coefficient and the constant term 2. Determine the factors of this product that add up to the coefficient of the middle term 3. Split the middle term and factor by grouping 4. Find the GCF of each binomial 5. Write the product of your factors Trinomials Product Method

Factor each polynomial completely.

4 Term Polynomials 1.Look for a perfect square trinomial 2.Group and factor the perfect square trinomial 3.Look for a difference of two squares 4.Factor the difference of two squares 5.Simplify

Factor each polynomial completely.

1.Grouping can be used with 4 terms 2.Group terms with a common factor 3.Find the GCF of each binomial 4.Factor out the common term 5.Write polynomial in factored form Factor by Grouping

Factor each polynomial completely.