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Section 6.5 Factoring by Grouping and a General Strategy for Factoring Polynomials

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6.5 Lecture Guide: Factoring by Grouping and a General Strategy for Factoring Polynomials Objective: Factor polynomials by the method of grouping. Objective: Determine the most appropriate technique for factoring a polynomial.

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Strategy for Factoring a Polynomial Over the Integers After factoring out the GCF (greatest common factor), proceed as follows. Binomials: Factor special forms: Difference of Two Squares Difference of Two Cubes Sum of Two Cubes is prime The sum of two squares is prime if x 2 and y 2 are only second-degree terms and have no common factor other than 1.

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Strategy for Factoring a Polynomial Over the Integers Trinomials: Factor the forms that are perfect squares: Perfect Square Trinomial; a Square of a Sum Perfect Square Trinomial; a Square of a Difference Otherwise, factor the trinomial by the grouping method. Polynomials of Four or More Terms : Factor by grouping Your goal upon finishing this section is to be able to use the various methods to factor each given polynomial without being told which type it is.

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Completely factor the following polynomials. 1.

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Completely factor the following polynomials. 2.

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Completely factor the following polynomials. 3.

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Completely factor the following polynomials. 4.

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Completely factor the following polynomials. 5.

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Completely factor the following polynomials. 6.

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Completely factor the following polynomials. 7.

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Completely factor the following polynomials. 8.

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Completely factor the following polynomials. 9.

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Completely factor the following polynomials. 10.

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Completely factor the following polynomials. 11.

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Completely factor the following polynomials. 12.

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Completely factor the following polynomials. 13.

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Completely factor the following polynomials. 14.

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Completely factor the following polynomials. 15.

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Completely factor the following polynomials. 16.

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Completely factor the following polynomials. 17.

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Completely factor the following polynomials. 18.

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Completely factor the following polynomials. 19.

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Completely factor the following polynomials. 20.

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