Problem 25 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 25

Divide as indicated. Check each answer by showing that the product of the divisor and the quotient, plus the remainder, is the dividend. $$\frac{4 y^{3}+8 y^{2}+5 y+9}{2 y+3}$$

Short Answer

Expert verified

The result of the division is $2y^2 +2y+ \frac{1}{2} + \frac{ \frac{3}{2} }{ 2y+3 } $

Step by step solution

Polynomial Division

To begin, divide the first term in the numerator $4y^3$ with the first term in the denominator $2y$ which gives us $2y^2$. Write this term as the first term of our quotient.

Subtracting

Multiply the entire divisor $(2y+3)$ by the partial quotient just obtained $(2y^2)$ and subtract this result from the original dividend. The result of this operation should be $4y^2+5y+9$.

Getting the next quotient term

Repeat the first step with the new polynomial: divide the first term $(4y^2)$ by the first term in the divisor $(2y)$ and write this term $2y$ as our next quotient term.

Second Subtraction

Multiply the divisor $(2y+3)$ by the updated quotient just obtained $(2y)$ and subtract this result from the updated dividend. The result of this operation should be $y+9$.

Getting the final quotient term

Repeat the first step with the new polynomial: divide the first term $(y)$ by the first term in the divisor $(2y)$, the quotient will be $ \frac{1}{2}$

Final Subtraction

As before, multiply the divisor $(2y+3)$ by the updated quotient just obtained $(\frac{1}{2})$ and subtract this result from the updated dividend. The result of this operation should be $ \frac{3}{2}$. This is our remainder.

Writing the Final Answer

The final quotient is the sum of all the partial quotients obtained, i.e., $2y^2 +2y+ \frac{1}{2}$. And the remainder we obtained is $ \frac{3}{2} $. Therefore the division result can be written as: $2y^2 +2y+ \frac{1}{2} + \frac{ \frac{3}{2} }{ 2y+3 } $

Check the Answer

To confirm that the answer is correct, verify that the product of the divisor and quotient, plus the remainder equals to the original dividend. The checking calculation would be $(2y+3)(2y^2 +2y+ \frac{1}{2})+\frac{3}{2} = 4y^3 + 8y^2 + 5y + 9 $. Thus, the answer 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. $$\frac{4 y^{3}+8 y^{2}+5 y+9}{2 y+3}$$

Short Answer

Step by step solution

Polynomial Division

Subtracting

Getting the next quotient term

Second Subtraction

Getting the final quotient term

Final Subtraction

Writing the Final Answer

Check the Answer

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