Chapter 11: Q36. (page 729)

Find each quotient.
$(5 x^{2} y^{2} - 10 x^{2} y + 5 x y) \div 5 x y$

Short Answer

Expert verified

The quotient is $x y - 2 x + 1$ .

Step by step solution

Step 1. Define the concept.

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

Step 2. Divide each term by 5xy.

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

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

Step 3. Simplify the expression.

Divide out the common factors and simplify.

$\begin{matrix} (5 x^{2} y^{2} - 10 x^{2} y + 5 x y) \div 5 x y = \frac{5 x^{2} y^{2}}{5 x y} + \frac{(- 10 x^{2} y)}{5 x y} + \frac{5 x y}{5 x y} \\ = x y - \frac{10 x^{2} y}{5 x y} + 1 \\ = x y - 2 x + 1 \end{matrix}$

Therefore, $(x^{3} + 7 x^{2} + 10 x - 6) \div (x + 3)$ is $x y - 2 x + 1$ .

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Find each quotient.
$(5 x^{2} y^{2} - 10 x^{2} y + 5 x y) \div 5 x y$

Short Answer

Step by step solution

Step 1. Define the concept.

Step 2. Divide each term by 5xy.

Step 3. Simplify the expression.

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Find each quotient.5x2y2−10x2y+5xy÷5xy

Short Answer

Step by step solution

Step 1. Define the concept.

Step 2. Divide each term by 5xy.

Step 3. Simplify the expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Discrete Mathematics

Decision Maths

Probability and Statistics

Mechanics Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Find each quotient.
$(5 x^{2} y^{2} - 10 x^{2} y + 5 x y) \div 5 x y$