Question

Polynomial long division: Problem Type 1

-Your answer should give the quotient and the remainder.-
**Algebra 1**

Answer 1

Quotient = 3x-5

Remainder = 3

Explanation:

For any long division, I use the DMS principle, divide, multiply, subtract.

(x+6) | 3x² + 13 x - 27

First of all, divide the first part of the equation by x. (which is 3x²)

You get 3x.

Now take your 3x and multiply it by (x+6)

You get 3x²+18x. You need to subtract this from your equation.

(3x² + 13 x - 27) - (3x² + 18x) = -5x - 27

One round of DMS complete

Now,

(x+6) | - 5x - 27

We again divide the first part only by x again. You get -5

We multiply -5 by (x+6)

-5x-30.

Let's subtract it from the equation.

(-5x-27) - (-5x-30) = - 5x - 27 + 5x + 30 = 3

Second round of DMS complete.

We cannot divide 3 further by (x+6) so this is it.

The remainder is 3.

Now we take our answers, which is 3x and - 5 and add them to get 3x-5. This is our quotient.