Explanation Approach: Division of a polynomial by binomial is done by using the synthetic division method is as below: 1. In this method take the coefficients of the polynomial in the descending powers of variable and if any term is missing than a zero must be used in that place. 2. Equate the divisor to zero and take the variable value for division. 3. Bring down the first coefficient of the dividend. 4. Multiply the first coefficient of the dividend by the divisor and write that value under the dividend. 5. Find the result by adding or subtracting. 6. The obtained results multiplied by the divisor again, and write that value under the dividend. 7. Repeat the process till the last coefficient and simplify. 8. Convert the coefficients of the last row to an equation of the quotient by decreasing the variable exponent by 1 and the last value of the row represents the remainder. Calculation: Consider the expression ( x 2 − 8 x + 12 ) ÷ ( x − 2 ) . First write the coefficients of the polynomial in the descending order. They are 1 , − 8 , 12 . Take the divisor and equate it to zero. That is, x − 2 = 0 Add 2 on both sides of the equation. x − 2 + 2 = 0 + 2 x − 2 + 2 = 2 x = 2 Arrange the coefficients in the descending order and write the divisor in the following way and simplify. 2 1 − 8 12 _ The calculation steps are as follows: Bring down 1 and multiply it with 2. 2 1 − 8 12 _ 1 The result is 2. Write it under the coefficient − 8 and subtract or add accordingly. The result is − 6 . 2 1 − 8 12 2 _ 1 − 6 Multiply the divisor 2 by − 6 and write the value under the coefficient 12

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ISBN: 9781285195728

Author: Jerome E. Kaufmann, Karen L. Schwitters

Publisher: Cengage Learning

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Chapter 4.5, Problem 53PS

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The quotient and remainder of the polynomials by performing the synthetic division.

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Chapter 4.5, Problem 52PS

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• Plane II is spanned by the vectors: P12 P2 = 1 • Subspace W is spanned by the vectors: W₁ = -- () · 2 1 W2 = 0

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The quotient and remainder of the polynomials by performing the synthetic division.

Solution Summary: The author explains how to find the quotient and remainder of polynomials by performing the synthetic division method.

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To Find: The quotient and remainder of the polynomials by performing the synthetic division.

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Chapter 4 Solutions

To Find:

The quotient and remainder of the polynomials by performing the synthetic division.