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NAME: ______________________________________________ DATE: ____________ Algebra 2: Lesson 7-4 Synthetic Division Learning Goals 1) How do we perform long division on polynomials? 2) How do we perform synthetic division on polynomials? 3) When can we use synthetic division when asked to divide polynomials? Do Now: Divide the following using long division. Divide x3 + 4x2 – 3x – 5 by x + 3 What is the degree of the following polynomials? 1) 5x2 – 7x + 5 2) 4x + 6x5 + 8x2 – 4 3) 8x7 – 4x2 + 9x10 ______ Now we will take the “do now” problem and divide by a method called synthetic division. Divide x3 + 4x2 – 3x – 5 by x + 3 using synthetic division. Step 1: Arrange the coefficients in descending order. {Remember to include placeholders for any missing variables}. Step 2: Write the constant of the divisor x – r {in this case -3} Step 3: Bring down the first coefficient. Step 4: Multiply the first coefficient by r {in this case -3}. Place that product under the 2nd coefficient. Step 5: Add the column. Then multiply that sum by r. Step 6: Repeat step 5 for all coefficients. Step 7: The final sum represents the remainder. The other numbers are the coefficients of the quotient polynomial which has degree one less than the dividend. Synthetic division can only be used when The divisor is a factor of the dividend when Practice: Divide each of the following using synthetic division. 1) Divide x3 – x2 + 2 by x + 1 2) Divide and find the factors of (2x3 – 3x2 + x) ÷ (x – 1). Divide each of the following using synthetic division. Then state whether the binomial is a factor of the polynomial. 3) (2x4 + 4x3 – x2 + 9) ÷ (x + 1) 4) (2x3 – 3x2 – 10x + 3) ÷ (x – 3) 5) Use synthetic division to find all of the factors of x3 + 6x2 – 9x – 54 if one of the factors is x – 3.