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

1 Answer
Jun 27, 2018

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)