Question

-Use synthetic division to find the result when 2x3 – 7x2 – 2x – 8 is divided byx-4

Answer 1

1) First, we write the problem in the division synthetic form. To do this:

• wake the constant term of the divisor with the opposite sign and write it to the left,

,

• we write the coefficients of the dividend to the right,

,

• we write down the first coefficient without changes.

2) We multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line). Then we add the obtained result to the next coefficient of the dividend, and write down the sum.

3) We repeat the previous step with the following column:

4) We repeat the previous step with the following column:

5) We have completed the table. We have obtained the following resulting coefficients: 2, 1, 2, 0. All the coefficients except the last one are the coefficients of the quotient, the last coefficient is the remainder.

`\begin{gathered} q(x)=2\cdot x^2+1\cdot x+2=2x^2+x+2, \\ R=0. \end{gathered}`

The result of the division is:

`q(x)+(R)/(x-4)=2x^2+x+2+(0)/(x-4)=2x^2+x+2.`

Answer

The result of the division is:

`2x^2+x+2`