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# Find the quotient and remainder using long division for

Find the quotient and remainder using long division for
\frac(x^3 -6 x^2 + 13 x -28)(x-4)

The quotient is ?
The remainder is  -8

Check my answer from where you posted the question earlier today.

### 2 Answers by Expert Tutors

George C. | Humboldt State and Georgetown graduateHumboldt State and Georgetown graduate
5.0 5.0 (2 lesson ratings) (2)
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Synthetic division:

4 |  1     -6     13     -28

4     -8       20

1    -2      5       -8

x^2   -2x    +5    -8/(x-4)

Roman C. | Masters of Education Graduate with Mathematics ExpertiseMasters of Education Graduate with Mathe...
4.9 4.9 (311 lesson ratings) (311)
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Using polynomial long division we get

x2  -  2x  +  5

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x - 4  |  x3 - 6x2 + 13x - 28

x3 - 4x2                  = x2(x - 4)

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-2x2 + 13x

-2x2 +   8x        = -2x(x - 4)

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5x - 28

5x - 20  = 5(x - 4)

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-8

Thus the quotient is x2 - 2x + 5. The remainder is -8, just as you said.