Question

Use synthetic division to find the quotient and remainder when 6x^4 + 9x^3 - 11x^2 + 20 is divided by x + 2 by completing the parts below.

Answer 1

Given:

6x^4 + 9x^3 - 11x^2 + 20 is divided by x + 2

a.)

To complete the given synthetic division table, we first carry down the leading coefficient and multiply the carry-down value by the zero of the denominator. We also carry the result up into the next column. The process is shown below:

Hence, the answer is shown above.

b)

We must note that the remainder is zero. Now, we write the answer in the form: quotient +remainder/(x+2)

So,

$\frac{6x^4+9x^3-11x+20}{x+2}=6x^3-3x^2-5x+10+\frac{0}{x+2}$