Chapter 11: Q37. (page 729)

Find each quotient.
$(48 y^{2} + 8 y + 7) \div (12 y - 1)$

Short Answer

Expert verified

The quotient is $4 y + 1 + \frac{8}{12 y - 1}$ .

Step by step solution

Step 1. Define the concept.

Method of long division is preferably used when the polynomial cannot be factored or if there are no common factors by which to divide.

Step 2. Use method of long division.

First divide the first term of the dividend, $48 y^{2}$ , by the first term of the divisor, $12 y$ .

$12 y - 1 4 y \begin{array}{l} 48 y^{2} + 8 y + 7 \\ \frac{48 y^{2} - 4 y}{12 y + 7} \end{array} (\begin{array}{l} 48 y^{2} \div 12 y = 4 y \\ Multiply 12 y - 1 and 4 y \\ Subtract. \end{array})$

Step 3. Simplify the expression.

To further simplify, divide the first term of the partial dividend, $12 y$ , by the first term of the divisor, $12 y$ . Repeat the process as many times required.

localid="1648066557321" role="math" $12 y - 1 4 y + 1 \begin{array}{l} 48 y^{2} + 8 y + 7 \\ \frac{48 y^{2} - 4 y}{\begin{array}{l} 12 y + 7 \\ 12 y - 1 \\ 8 \end{array}} \end{array}$

Therefore, $(48 y^{2} + 8 y + 7) \div (12 y - 1)$ is $4 y + 1$ with a remainder of 8. This answer can be written as $4 y + 1 + \frac{8}{12 y - 1}$ .

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Find each quotient.
$(48 y^{2} + 8 y + 7) \div (12 y - 1)$

Short Answer

Step by step solution

Step 1. Define the concept.

Step 2. Use method of long division.

Step 3. Simplify the expression.

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Find each quotient.48y2+8y+7÷12y−1

Short Answer

Step by step solution

Step 1. Define the concept.

Step 2. Use method of long division.

Step 3. Simplify the expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Probability and Statistics

Calculus

Applied Mathematics

Discrete Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

Find each quotient.
$(48 y^{2} + 8 y + 7) \div (12 y - 1)$