Problem 12 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 12

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

Short Answer

Expert verified

The solution to the division is $y + 3$, verified by the product of the divisor and quotient equalling the original dividend.

Step by step solution

Arrange the Dividend and Divisor

Look at the dividend and divisor. Arrange them for polynomial division: divide $-8y + y^2 - 9$ by $y - 3$. Make sure that both are written in descending order of their powers.

Polynomial Division

Begin dividing. The first term of the dividend is divided by the first term of the divisor. So, $y^2/y = y$. Write this as the first term of quotient. Multiply the divisor $y -3$ by $y$ (from our quotient) and subtract this result from the dividend. It gives the new dividend $3y - 9$. Repeat the process for the new dividend. Divide the first term of the new dividend by the first term of the divisor which results in 3 and write it as the second term of the quotient.

Verify the Answer

Check that the product of the divisor and the quotient, plus the remainder, equals the original dividend. Multiply the quotient $y + 3$ by the divisor $y - 3$. Since there's no remainder in our division, we don't need to add any remainder. The result is $-8y + y^2 - 9$ which is the same as the original dividend, so our answer is correct.

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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. $$\frac{-8 y+y^{2}-9}{y-3}$$

Short Answer

Step by step solution

Arrange the Dividend and Divisor

Polynomial Division

Verify the Answer

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