Question

How do you divide `(x^3+4x^2-3x-12)/(x-3)`?

Answer 1

Below is your division, in long division from.

Explanation:

Thus, `x^3 + 4x^2 - 3x - 12 = (x - 3)(x^2 + 7x + 18)`

How does it work?

The quotient is found by performing a division between the leading term in the dividend and the divisor.

For example the leading term in the dividend is `x^3` (in the first step) and that of the divisor is `x`

`x^3/x`

`x^2`

Take the second part of the quotient. Once you do your subtraction, you will get `7x^2` as the leading term off the dividend. Your divisor's leading term is still `x`

Thus, `(7x^2)/x = 7x`

What you have to do with long division is to remember to put the leading term with an equal degree in each of the steps and to subtract, so that you cancel out the leading terms and that you are left with the second terms. You will then carry down numbers from the dividend, working from left to right.

You must go all the way to the end, in a goal to find the remainder, which will be a constant term. In your case, the remainder is 42.

Practice exercises:

Evaluate the following long division.

Good luck!