Dividing Polynomials

**Hi888** · July 31st 2008, 07:13 AM

1. (m^4 + 3m^3 - 9m^2 - 21m +8) / (m^2 - 7)

2. (-2d^3 - 4d^2 + d^4 - 10d + 3) / (d^2 + 3 + 2d)

Please help me with this given items. I'll be using them as my reference guide because I cant understand it.

Thanks in advance!

**Soroban** · July 31st 2008, 10:09 AM

Hello, Hi888!

We're expected to know how to do long division . . .

$1.\;\;(m^4 + 3m^3 - 9m^2 - 21m +8) \div (m^2 - 7)$

$\begin{array}{ccccccc} & & & & m^2 & +3m & -2 \\ & & --- & --- & --- & --- & --- \\ m^2-7 & ) & m^4 & +3m^3 & -9m^2 & -21m & +8 \\ & & m^4 & & -7m^2 \\ & & --- & --- & --- \\ & & & 3m^3 & -2m^2 & -21m \\ & & & 3m^3 & & -21m \\ & & & --- & --- & --- \\ & & & & -2m^2 & & +8 \\ & & & & -2m^2 & +14 \\ & & & & --- & --- & --- \end{array}$

. . . . . . . . . . . . . . . . . . . . . . . . . . . . $-6$
Answer: . $m^2 + 3m - 2 - \frac{6}{m^2-7}$

$2.\;\;(-2d^3 - 4d^2 + d^4 - 10d + 3) \div (d^2 + 3 + 2d)$

$\begin{array}{ccccccc} & & & & d^2 & -4d & +1 \\ & & -- & -- & -- & -- & -- \\ d^2+2d+3 & ) & d^4 & -2d^3 & -4d^2 & -10d & +3 \\ & & d^4 & +2d^3 & +3d^2 \\ & & -- & -- & -- \\ & & & -4d^3 & -7d^2 & -10d \\ & & & -4d^3 & -8d^2 & -12d \\ & & & -- & -- & -- \\ & & & & d^2 & +2d & + 3 \\ & & & & d^2 & +2d & + 3 \\ & & & & -- & -- & -- \end{array}$

. . . . . . . . . . . . . . . . . . . . . . . . . . .0
Answer: . $d^2 - 4d + 1$

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