Question

How do you divide `(x^3+2x^2-11x-12)/(x^2-3x+2)`?

Answer 1

Long divide coefficients to find:

`(x^3+2x^2-11x-12)/(x^2-3x+2) = x+5+(2x-22)/(x^2-3x+2)`

Explanation:

You can just divide the coefficients like this:

The process is similar to long division of numbers.

Note that if there were any 'missing' powers of `x` in the dividend or divisor then we would have to include `0`'s for them.

Write the dividend `1,2,-11,-12` under the bar and the divisor `1,-3,2` to the left.

Choose the first term `color(blue)(1)` of the quotient so that when multiplied by the divisor, the resulting leading term (`1`) matches the leading term (`1`) of the dividend.

Write the product `1,-3,2` of this first term of the quotient and the divisor under the dividend and subtract to give a remainder `5,-13`.

Bring down the next term `-12` from the dividend alongside it to give your running remainder `5,-13,-12`.

Choose the next term `color(blue)(5)` of the quotient so that when multiplied by the divisor, the resulting leading term (`5`) matches the leading term (`5`) of the remainder.

Write the product `5,-15,10` of this second term of the quotient and the divisor under the running remainder and subtract to give a remainder `2,-22`.

There are no more terms to bring down from the dividend, so this is our final remainder.

We find:

`(x^3+2x^2-11x-12)/(x^2-3x+2) = x+5+(2x-22)/(x^2-3x+2)`