Explanation Given: The polynomial is P ( x ) = x 3 − 9 x 2 + 15 x + 25 . The divisor is d ( x ) = x − 5 . Procedure used: Long division method: Step 1: Ensure that the polynomial is written in the descending order with respect to its degree and if any terms are missing in the order, add the terms with the co-efficient zero. Step 2: Divide the highest-degree term of the dividend by the highest-degree term of the divisor and align the like terms vertically. Step 3: Multiply the divisor and the answer obtained in the step 2. Step 4: Subtract the product obtained in step 3 from the dividend and bring down the next term. Step 5: Continue the above steps 1 to 4 until there are no terms left to bring down. Calculation: Divide the polynomial P ( x ) = x 3 − 9 x 2 + 15 x + 25 by x − 5 . Use the above procedure to find the quotient of the given expression. x − 5 x 2 − 4 x − 5 x 3 − 9 x 2 + 15 x + 25 x 3 − 5 x 2 _ − 4 x 2 + 15 x − 4 x 2 + 20 x _ − 5 x + 25 − 5 x + 25 _

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Chapter 4.3, Problem 8E

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To find: The quotient Q(x) and the remainder R(x) by using long division when P(x) is divided by d(x) and then express P(x) in the form d(x)⋅Q(x)+R(x).

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Chapter 4.3, Problem 7E

Chapter 4.3, Problem 9E

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The quotient Q ( x ) and the remainder R ( x ) by using long division when P ( x ) is divided by d ( x ) and then express P ( x ) in the form d ( x ) ⋅ Q ( x ) + R ( x ) .

Solution Summary: The author explains how to find the quotient of the given expression by using long division.

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To find: The quotient Q(x) and the remainder R(x) by using long division when P(x) is divided by d(x) and then express P(x) in the form d(x)⋅Q(x)+R(x).

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