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Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 11: Q36. (page 729)

Find each quotient.
$(5 x^{2} y^{2} 鈭� 10 x^{2} y + 5 x y) 梅 5 x y$

Short Answer

Expert verified

The quotient is $x y 鈭� 2 x + 1$ .

Step by step solution

01

Step 1. Define the concept.

To divide a polynomial by a monomial, divide each term of the polynomial by the monomial.

02

Step 2. Divide each term by 5xy.

First write as a fraction, then divide each term by $5 x y$ .

role="math" localid="1648065397746" $(5 x^{2} y^{2} 鈭� 10 x^{2} y + 5 x y) 梅 5 x y = \frac{5 x^{2} y^{2} 鈭� 10 x^{2} y + 5 x y}{5 x y} = \frac{5 x^{2} y^{2}}{5 x y} + \frac{(鈭� 10 x^{2} y)}{5 x y} + \frac{5 x y}{5 x y}$

03

Step 3. Simplify the expression.

Divide out the common factors and simplify.

$\begin{matrix} (5 x^{2} y^{2} 鈭� 10 x^{2} y + 5 x y) 梅 5 x y = \frac{5 x^{2} y^{2}}{5 x y} + \frac{(鈭� 10 x^{2} y)}{5 x y} + \frac{5 x y}{5 x y} \\ = x y 鈭� \frac{10 x^{2} y}{5 x y} + 1 \\ = x y 鈭� 2 x + 1 \end{matrix}$

Therefore, $(x^{3} + 7 x^{2} + 10 x 鈭� 6) 梅 (x + 3)$ is $x y 鈭� 2 x + 1$ .

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Most popular questions from this chapter

Determine whether each table or equation represents an inverse or a direct variation. Explain.

$x y = 4$

Find the product.

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$y = \frac{2}{x 鈭� 4}$

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