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**5.5 Apply the Remainder and Factor Theorem**

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Long Division Polynomial Long Division: process used to divide polynomials. Divide f(x) = 3x4 – 5x + 4x – 6 by x3 – 3x + 5

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**Divide f(x) = x3 + 5x – 7x + 2 by x – 2**

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**Solve Using Long Division**

(1) (2x4 + x3 + x – 1) ÷ (x2 + 2x – 1) (2) (x3 – x2 + 4x – 10) ÷ (x + 2)

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Synthetic Division Synthetic Division can be used to divide any polynomial by a divisor of the form x – k. (EX) Divide 2x3 + x2 – 8x + 5 by x + 3 Step 1: Set x + 3 = 0 and solve for x. Step 2: Use Synthetic substitution to find the remainder. Step 3: All numbers below the line will be used for the final answer.

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Factor Theorem If synthetic division is used and the remainder is determined to be 0, then the divisor (x – k) is a factor of the polynomial. If (x – k) is a factor, then you can find the remaining factors of the polynomial by using synthetic substitution.

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Factor the Polynomial Factor f(x) = 3x3 – 4x – 28x – 16 completely given that x + 2 is a factor. Step 1: Use synthetic substitution Step 2: Factor the Quotient Reminder: The remainder must be zero before factoring the quotient.

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Practice Problems Page 364 (3-6)

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CW/HW Page 366 (9,11,13,15,21,23)

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