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Section 1. Finding Factors. Factorizing algebraic expressions is a way of turning a sum of terms into a product of smaller ones. The product is a multiplication of the factors. Sometimes it helps to look at a simpler case before venturing into the abstract. The number 48 may be written as a product in a number of di erent ways:

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FACTORING POLYNOMIALS 1) First determine if a common monomial factor (Greatest Common Factor) exists. Factor trees may be used to find the GCF of difficult numbers. Be aware of opposites: Ex. (a-b) and (b-a) These may become the same by factoring -1 from one of them.

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When we introduced factoring on polynomials, we relied on finding a factor which was shared by all the terms. If we don’t have a single shared factor, there are other techniques we can use to factor a polynomial. This module introduces the technique of grouping, which can be applied to factor polynomials in certain situations.

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Factoring trinomials of form ax2 + bx+ c The Grouping Method to factor trinomials of form ax2 + bx+ c: 1.Determine the grouping number ac. 2.Find two numbers whose product is ac and sum is b. 3.Use these numbers to write bx as the sum of two terms. 4.Factor by grouping. 5.Check your answer by multiplying out. Di erence of Squares a2 b2 = (a b ...

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Factoring By Grouping Date_____ Period____ Factor each completely. 1) 8 r3 − 64 r2 + r − 8 2) 12 p3 − 21 p2 + 28 p − 49 3) 12 x3 + 2x2 − 30 x − 5 4) 6v3 − 16 v2 + 21 v − 56 5) 63 n3 + 54 n2 − 105 n − 90 6) 21 k3 − 84 k2 + 15 k − 60 7) 25 v3 + 5v2 + 30 v + 6 8) 105 n3 + 175 n2 − 75 n − 125 9) 96 n3 − 84 n2 + 112 n − 98 10) 28 v3 + 16 v2 − 21 v − 12 11) 4v3 ...

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4.4 Factoring Polynomials. Essential Question. How can you factor a polynomial? Factoring Polynomials. Work with a partner. Match each polynomial equation with the graph of its related polynomial function. Use the x-intercepts of the graph to write each polynomial in factored form. Explain your reasoning. x2 5x 4 0. = x3 2x2 x 2 0. − − + =

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Factoring Quadratic Expressions Date_____ Period____ Factor each completely. 1) x2 − 7x − 18 2) p2 − 5p − 14 3) m2 − 9m + 8 4) x2 − 16 x + 63 5) 7x2 − 31 x − 20 6) 7k2 + 9k 7) 7x2 − 45 x − 28 8) 2b2 + 17 b + 21 9) 5p2 − p − 18 10) 28 n4 + 16 n3 − 80 n2-1-©4 f2x0 R1D2c TKNuit 8aY ASXoqfyt GwfacrYed fL KL vC6. u g eArl kl A mrviZgLhBt Qsd Jr leospeGr7vHehd k.5 e ...

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Factoring Polynomials by Grouping. You have used the Distributive Property to factor out a greatest common monomial from a polynomial. Sometimes, you can factor out a common binomial. You may be able to use the Distributive Property to factor polynomials with four terms, as described below.

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Factoring: All Techniques Combined (Hard) Date_____ Period____ Factor each. 1) x3 − 5x2 − x + 5 2) x4 − 2x2 − 15 3) x6 − 26 x3 − 27 4) x6 + 2x4 − 16 x2 − 32 5) x4 − 13 x2 + 40 6) x9 − x6 − x3 + 1 7) x6 − 4x2 8) x4 + 14 x2 + 45-1-©h G2B05162 P 7KguYt4a L 9SVo3fHt0wGatr TeG XLELeC W.y T lA ulClK Ir Niig shTt2sL BrLeesTeIr 0vxe dK.T g NMaPd4e a 5wYiSteh k xIfn jfBiJn 2irt ...