- #1

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X^3 + X - 71 = (X^2 + 4X + 16)Q(X) + R(X), where Q and R are polynomials. Decide which they are.

I got that Q(X) = (X + 1/4) and that R(X) = - 75, but apparently it is wrong. I am stuck and don't know what to do.

Thanks in advance.

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- Thread starter stefanB
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- #1

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- 0

X^3 + X - 71 = (X^2 + 4X + 16)Q(X) + R(X), where Q and R are polynomials. Decide which they are.

I got that Q(X) = (X + 1/4) and that R(X) = - 75, but apparently it is wrong. I am stuck and don't know what to do.

Thanks in advance.

- #2

EnumaElish

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- #3

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Substitute it into the equation and you'll get (X^2 + 4X + 16)(Ax + B) + (Cx + D).

The next step is for you to expand the above expression as per normal. Then you group the terms according to the degree of x and then equate the coefficients accordingly with X^3 + X - 71.

As a check, you should get A=1.

- #4

Dick

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