# Purchase MAT 104 - Chapter R Section 5 - Factoring polynomials (16 pages)

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## Chapter R Section 5 - Factoring polynomials

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## Chapter R Section 5 - Factoring polynomials

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Lecture Notes

Pages:
16
School:
SUNY College at Purchase
Course:
Mat 104 - Mathematics with Business Application
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Chapter R Section 5 Factoring Polynomials In this section we will Factor out the GCF Greatest Common Factor Factor by Grouping 2 Factor Trinomials of the Form x bx c 2 ax bx c Factor Trinomials of the Form Factor the Sum and Difference of Two Perfect Cubes R 5 Factoring Polynomials In the previous section we learned how to multiply polynomials in this section we will reverse the operation of multiplication by finding the factors of a known product If one number a divides evenly into another number b then a is called a factor of b example Because 3 divides evenly into 24 3is a factor of 24 multiply the polynomials factor the polynomial 3x 2 x 1 R 5 Factoring Polynomials Factor Out the GCF 2 6 x 3x We are in essence un distributing Examples Factor out the GCF greatest common factor 60 x 2 y 48 xy 2 72 x3 y R 5 Factoring Polynomials Factor Out the GCF 5 3 x 7 x 3x 7 Examples Factor by grouping 6 x 2 9 x 4 x 6 R 5 Factoring Polynomials Factor by Grouping x 3 4 x 2 2 x 8 multiply the polynomials x 2 x 3 factor the polynomial sum product x2 5x 6 We are in essence un FOIL ing Factoring Trinomials with a leading coefficient of 1 Write the trinomial in descending order for the first variable alphabetically Write the factorizations of the third term of the trinomial Pick the factorization where the sum of the factors is equal to the coefficient of the middle term R 5 Factoring Polynomials Factor Trinomials of the Form x 2 bx c Examples Factor each trinomial y 2 12 y 36 2 x 16 10 x Some Handy Dandy Special Product Formulas Perfect Squares x 2ax a x a Difference of Two Squares x 2 a 2 x a x a 2 2 x 2ax a x a 2 2 2 2 some perfect squares 1 4 9 16 25 36 49 64 81 100 121 144 R 5 Factoring Polynomials Factor Trinomials of the Form x 2 bx c Examples Factor each trinomial 2 x 9 9 y 2 64 R 5 Factoring Polynomials Factor Trinomials of the Form x 2 bx c Factoring Trinomials with a leading coefficient other than 1 2 methods Guess and Check Method Write the trinomial in descending order

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