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Dividing Polynomials: Synthetic Division
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Essential Question How do I use synthetic division to determine if something is a factor of a polynomial?
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Khan Academy Videos https://www.youtube.com/watch?v=1byR9 UEQJN0 https://www.youtube.com/watch?v=1byR9 UEQJN0 https://www.youtube.com/watch?v=3Ee_hu KclEQ https://www.youtube.com/watch?v=3Ee_hu KclEQ
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Synthetic Division - To use synthetic division: There must be a coefficient for every possible power of the variable. The divisor must have a leading coefficient of 1. divide a polynomial by a polynomial
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Step #1: Write the terms of the polynomial so the degrees are in descending order. Since the numerator does not contain all the powers of x, you must include a 0 for the
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Step #2: Write the constant r of the divisor x-r to the left and write down the coefficients. Since the divisor is x-3, r=3 50-416
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5 Step #3: Bring down the first coefficient, 5.
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5 Step #4: Multiply the first coefficient by r, so and place under the second coefficient then add. 15
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5 Step #5: Repeat process multiplying the sum, 15, by r; and place this number under the next coefficient, then add. 45 41
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5 15 45 41 Step #5 cont.: Repeat the same procedure. 123 124 372 378 Where did 123 and 372 come from?
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Step #6: Write the quotient. The numbers along the bottom are coefficients of the power of x in descending order, starting with the power that is one less than that of the dividend. 5 15 45 41 123 124 372 378
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The quotient is: Remember to place the remainder over the divisor.
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Ex 7: Step#1: Powers are all accounted for and in descending order. Step#2: Identify r in the divisor. Since the divisor is x+4, r=-4.
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Step#3: Bring down the 1st coefficient. Step#4: Multiply and add. -5 Step#5: Repeat. 20 4-4 0 8 10-210
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Assignment Complete the worksheet.
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