Problem 19 Divide as indicated. Check each ... [FREE SOLUTION]

91影视

Introductory Algebra for College Students

Robert Blitzer

$Math Studyset 91影视 Explanations$ Math

6 Edition

Chapter 5: Problem 19

Divide as indicated. Check each answer by showing that the product of the divisor and the quotient, plus the remainder, is the dividend. $$\frac{3 y-y^{2}+2 y^{3}+2}{2 y+1}$$

Short Answer

Expert verified

The quotient when $2y^3 - y^2 + 3y + 2$ is divided by $2y + 1$ is $y^2 - y + 2$, with remainder $0$

Step by step solution

Arrange the Polynomial for Long Division

Before starting, it's important to arrange the terms in the polynomial in descending order of the degree. Hence, arrange the polynomial as $2y^3 - y^2 + 3y + 2$. And similarly, $2y + 1$.

Perform Long Division

Now, let's begin the long division of polynomials. The first term of the polynomial dividend is divided by the first term of the divisor to get the first term of the quotient. This process is then repeated, including the subtraction until all terms in the dividend have been considered. The result of the division is: $y^2 - y + 2$, with remainder $0$.

Check your answer

To verify this result, we multiply the divisor by the quotient and add any remainder. Doing this, $(2y+1) * (y^2 - y + 2) + 0 = 2y^3 - y^2 + 3y + 2 $, which is the original dividend. So, the result of our polynomial division is verified.

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91影视

Divide as indicated. Check each answer by showing that the product of the divisor and the quotient, plus the remainder, is the dividend. $$\frac{3 y-y^{2}+2 y^{3}+2}{2 y+1}$$

Short Answer

Step by step solution

Arrange the Polynomial for Long Division

Perform Long Division

Check your answer

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