3.6_FactoringPolynomials

3.6_FactoringPolynomials - f(x is divided by x – a the...

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MHF 4U0 3.6 Factoring Polynomials Investigation Complete the table by dividing the polynomial P(x) = 2 x 3 – 2 x 2 – 3 x + 3 by the given divisors. Divisor, x – a a Remainder P(a) (a) x – 3 (b) x – 2 (c) x + 2 (d) x – 1 (e) x + 3 (f) x + 1 Reflection Questions 1. Examine the remainders and the values of P(a) when P(x) is divided by x – a. What do you notice? 2. For which values of a in your table is ( x a ) a factor of P(x)? How do you know? 3. How can you use your answers above to determine i. the remainder when P(x) is divided by x – a? ii. the factors of P(x)? Pg. 1/3
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MHF 4U0 3.6 Factoring Polynomials The Remainder Theorem Example #1: Consider the polynomial f(x) = x 3 + 3x 2 – 2x + 1. (a) Determine the remainder when (b) Determine the remainder when f(x) is divided by x + 1. f(x) is divided by 2x + 3. The Factor Theorem Example #2: Verify that x – 1 is a factor of f(x) = 2 x 3 – 2 x 2 – 3 x + 3 using the Factor Theorem. Pg. 2/3 When a polynomial,
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Unformatted text preview: f(x) , is divided by x – a, the remainder is equal to f ( a ) . When a polynomial, f(x) , is divided by a x – b, the remainder is equal to a b f . If the remainder is equal to zero , then x – a is a factor of f(x) . A polynomial f(x) has x – a as a factor if and only if f(a) = 0. Meaning…? “if and only if” means the following… • if x – a is a factor of f(x), then f(a) = 0 • if f(a) = 0, then x – a is a factor of f(x) MHF 4U0 3.6 Factoring Polynomials Example #3: (a) Factor f(x) = 2 x 3 – 3 x 2 – 5 x + 6. (b) Sketch the graph of the function using the factored form. Example #4: If P(x) = m x 3 + g x 2 – x + 3 is divided by x + 1, the remainder is 3. When P(x) is divided by x + 2, the remainder is –7. What are the values of m and g ? Assigned Work: page 176 #3, 4cd, 5c, 6be, 7be, 8be, 10, 14 Pg. 3/3...
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This note was uploaded on 01/14/2012 for the course MAT 107 taught by Professor Sda during the Spring '11 term at Beacon FL.

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3.6_FactoringPolynomials - f(x is divided by x – a the...

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