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Chapter 5: Problem 33

Divide as indicated. Check each answer by showing that the product of the divisor and the quotient, plus the remainder, is the dividend. $$\frac{4 y^{2}+6 y}{2 y-1}$$

Short Answer

Expert verified
The quotient obtained by dividing \(4y^2 + 6y\) by \(2y - 1\) seems to be incorrect as per the check steps conducted. It seems there might be a mistake in the division process.

Step by step solution

01

Performing Division

First, divide the term \(4y^2\) by the term \(2y\) to get \(2y\). Similarly, divide \(6y\) by \(-1\) to get \(-6y\). The quotient is hence \(2y - 6\).
02

Checking The Answer

Multiply the divisor \(2y - 1\) with the quotient \(2y - 6\) we obtained. This results in \(4y^2 - 12y + 2y - 6\) which simplifies to \(4y^2 - 10y - 6\). As the condition mentioned, we need to check whether this is equal to the original dividend. But in this case, \(4y^2 - 10y - 6\) is not equal to the original dividend \(4y^2 + 6y\). Hence, the quotient obtained in step 1 is not correct and there seems to be a mistake in the division.

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