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Setler [38]
3 years ago
9

Use long division to divide x^3+x^2-2x+14 by x+3

Mathematics
1 answer:
bekas [8.4K]3 years ago
8 0

First, x^3=x^2\cdot x, and if we multiply x+3 by x^2 we get

x^3+3x^2

Subtracting this from the numerator gives a remainder of

-2x^2-2x+14

Next, -2x^2=-2x\cdot x, and if we multiply x+3 by -2x we have

-2x^2-6x

and subtracting this from the previous remainder, we end up with a new remainder of

4x+14

Next, 4x=4\cdot x, and if we multiply x+3 by 4 we get

4x+12

Subtracting from the previous remainder, we get a new remainder of

2

which contains no more factors of x, so we're done.

So,

\dfrac{x^3+x^2-2x+14}{x+3}=x^2-2x+4+\dfrac2{x+3}

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