Polynomial-Factoring

# Polynomial-Factoring - Factoring Polynomials In order to...

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From MathMotivation.com – Permission Granted For Use and Modification For Non-Profit Purposes Factoring Polynomials In order to factor a polynomial like f(x) = x 3 + 2x – 3, you first need to be able to divide the polynomial by a factor. Once you divide by a factor, you can rewrite f(x) as the product of your divisor times the quotient obtained. So first, we must review polynomial division. Long Polynomial Division: To divide a polynomial by another polynomial, you use the Division Algorithm in the same way you would divide 162 ÷ 5 . You Divide, Multiply, Subtract, and Carry Down, repeatedly as shown below. Divide 162 ÷ 5 = 3 (tens) Multiply 3 (tens) 5 = 30 5 = 15 (tens) Subtract 16 (tens) – 15 (tens) = 1 (ten) Carry Down 2 Divide 12 ÷ 5 = 2 Multiply 2 5 = 10 Subtract 12 – 10 = 2 Nothing left to carry down, so we stop. Our answer is 32 r 2 or 32 2/5 You can apply the same procedure to the division of two polynomials, (x 4 – 2x 2 + x –2) ÷ (x 2 + x – 4) First, however, we must insert zero placeholders for missing terms and rewrite as (x 4 + 0x 3 – 2x 2 + x –2) ÷ (x 2 + x – 4) Now, set up as a standard division problem and repeat the steps Divide, Multiply, Subtract, Carry Down over and over until the divisor no longer may be divided into the result at the bottom. Step 1 – Divide leading term of dividend x 4 by leading term of divisor x 2 . The result is x 2 and this is the first part of the answer. Step 2 – Multiply your answer x 2 by divisor (x 2 + x – 4) using the Distributive Property to get x 4 + x 3 4x 2 . Place under dividend. Step 3 – Subtract x 4 + x 3 – 4x 2 from divisor. Remember to correctly distribute the negative through the polynomial and add the opposite of each term! Step 4 –

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## This note was uploaded on 11/05/2011 for the course ANTHRO 101 taught by Professor Crandall during the Fall '09 term at BYU.

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Polynomial-Factoring - Factoring Polynomials In order to...

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