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Use synthetic division to find .Write your answer in the form , where is a polynomial, is an integer, and is a linear polynomial. Simplify any fractions.______
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Q. Use synthetic division to find .Write your answer in the form , where is a polynomial, is an integer, and is a linear polynomial. Simplify any fractions.______
- Set up synthetic division: Set up synthetic division by writing the root of the divisor , which is , to the left of a vertical bar. Then write the coefficients of the dividend to the right: .
- Bring down leading coefficient: Bring down the leading coefficient () to the bottom row.
- Multiply and write result: Multiply the root by the number just brought down and write the result under the next coefficient .
- Add numbers in second column: Add the numbers in the second column to get . Write this number below the line.
- Multiply and write result: Multiply the root by the new number in the bottom row and write the result under the next coefficient .
- Add numbers in third column: Add the numbers in the third column to get . Write this number below the line.
- Identify quotient polynomial: The numbers in the bottom row are the coefficients of the quotient polynomial. Since we started with a quadratic polynomial and divided by a linear polynomial, the result is a linear polynomial with coefficients and .
- Write quotient polynomial: Write the quotient polynomial using the coefficients from the bottom row: .
- Calculate remainder: The remainder is the number in the bottom right corner, which is . So, .
- Write final answer: Write the final answer in the form . Since the remainder is , the division is exact and the result is just the quotient polynomial: .
