Explanation Given: ( x 2 − 4 x − 12 ) ÷ ( x − 6 ) Key Concept Applied: Synthetic division is another method of dividing polynomial other than long division. We can use synthetic division whenever you need to divide a polynomial function by a binomial of the form x − c , where c is a constant. Here are the steps required for Synthetic Division of a Polynomial: Step 1: In order to set up the synthetic division, we should set the divisor to zero and solve it to find the number to place in the division box. Step 2: Then write the coefficients of the dividend to the right, across the top. Include any 0's that were inserted in for missing terms. Step 3: Once the problem is set up correctly, bring the leading coefficient (first number) straight down. Write down the first coefficient without changes. Step 4: Multiply the number in the division box with the number you brought down and put the result in the next column. That is multiply c by the value just written on the bottom row. Place this value right beneath the next coefficient in the dividend: Step 5: Add the two numbers together and write the result in the bottom of the row. Step 6: Repeat steps 4 and 5 until you reach the end of the problem. Step 7: Write the final answer. The final answer is made up of the numbers in the bottom row with the last number being the remainder and the remainder must be written as a fraction. The variables or x’s start off one power less than the original denominator and go down one with each term. Formula used: D I V I D E N D = ( Q U O T I E N T ) ( D I V I S O R ) + R E M A I N D E R Calculation: Description ( x 2 − 4 x − 12 ) ÷ ( x − 6 ) Step 1: In order to set up the synthetic division, we should set the divisor to zero and solve it to find the number to place in the division box. x − 6 = 0 x − 6 + 6 = 0 + 6 x − 6 + 6 = 0 + 6 x = 6 6 Step 2: Then write the coefficients of the dividend to the right, across the top. Include any 0's that were inserted in for missing terms. x 2 − 4 x − 12 ↓ ↓ ↓ 6 1 − 4 − 12 _ Step 3: Once the problem is set up correctly, bring the leading coefficient (first number) straight down. Write down the first coefficient without changes. 6 1 − 4 − 12 ↓ _ 1 Step 4: Multiply the number in the division box with the number you brought down and put the result in the next column. That is multiply c by the value just written on the bottom row. Place this value right beneath the next coefficient in the dividend. 6 1 − 4 − 12 ↓ 6 _ 1 S c r a t c h w o r k 6 × 1 = 6 Step 5: Add the two numbers together and write the result in the bottom of the row. 6 1 − 4 − 12 ↓ 6 _ 1 2 S c r a t c h w o r k − 4 + 6 = 2 Step 6: Multiply the number in the division box with the number you brought down and put the result in the next column

5th Edition

ISBN: 9781259610233

Author: Julie Miller, Molly O'Neill, Nancy Hyde

Publisher: McGraw-Hill Education

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Chapter 4.4, Problem 54PE

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The result obtained by dividing polynomial using synthetic division

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Chapter 4.4, Problem 53PE

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