Question

use synthetic division to find the awnser write the quotient and write any remainders in fraction form (3x^3-x^2-9x+5)÷(x-2)

Answer 1

The given expressions are

`\begin{gathered} 3x^3-x^2-9x+5 \\ x-2 \end{gathered}`

We have to use the coefficients only to divide. Remember that the number 2 must multiply all the numbers in the quotient. The synthetic division would be:

x3 x2 x

| 3 -1 -9 5

2 | 6 10 2

3 5 1 7

Notice that the remainder is 7, the quotient would be the coefficients under the line.

The quotient is

`3x^2+5x^{}+1`

Notice that the quotient doesn't include the number 7 because that's the remainder.

The remainder is 7.

We can express the quotient, the remainder, and the divisor as follows:

`(3x^3-x^2-9x+5)/(x-2)=3x^2+5x+1+(7)/(x-2)`