Question

Divide the following polynomial and place the answer in the proper location on the grid. Write the remainder as a tion.8²−4y+1/2y−1

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a) Quotient: 4y−2, Remainder: 11/2y−1
b) Quotient: 4y+2, Remainder: 11/2y−1
c) Quotient: 4y−2, Remainder: 9/2y−1
d) Quotient: 4y+2, Remainder: 9/2y−1
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Answer 1

To divide the polynomial 8²−4y+1 by 2y−1, use long division. The quotient is 4y−2 and the remainder is 1.

Step-by-step explanation:

To divide the polynomial 8²−4y+1 by 2y−1, we can use long division. First, divide the first term of the polynomial, 8², by the first term of the divisor, 2y. This gives us 4y. Multiply the divisor, 2y−1, by the quotient, 4y, and subtract it from the polynomial:

8²−4y+1 - (4y * (2y−1))

This leaves us with a new polynomial, 8²−4y+1 - (8y²-4y). Continue dividing and subtracting until there are no more terms left in the polynomial. The quotient is the sum of all the quotients obtained during the division process, which is 4y−2. The remainder is the final polynomial after the division, which is 1. So the correct answer is option a) Quotient: 4y−2, Remainder: 1.