Question

How do you divide `(- 7x ^ { 3} + 58x ^ { 2} - 65x - 22) \div ( x - 7)`?

Answer 1

Perform long division by dividing repeatedly one leading term into the other and then subtracting off the multiple of the whole divisor to leave a remainder.

Explanation:

Perform long division by dividing repeatedly one leading term into the other and then subtracting off the multiple of the whole divisor to leave a remainder.

`x` goes into `-7x^3` `-7x^2` times. Subtract off:
`(-7x^3+58x^2-65x-22)-(-7x^2)(x-7)=`
`-7x^3+58x^2-65x-22+7x^3-49x^2=`
`9x^2-65x-22`

`x` goes into `9x^2` `9x` times. Subtract off:
`(9x^2-65x-22)-9x(x-7)=`
`9x^2-65x-22-9x^2+63x=`
`-2x-22`

`x` goes into `-2x` `-2` times. Subtract off:
`(-2x-22)-(-2)(x-7)=`
`-2x-22+2x-14=`
`-36`

So we are left with a remainder of 36 afterwards, into which `x-7` does not divide. Putting these together, we get:

`(-7x^3+58x^2-65x-22)/(x-7)=-7x^2+9x-2-36/(x-7)`