Question

Use synthetic division to (x^3-x^2-17x-15)/(x-5). What is the quotient?

Answer 1

x^3-x^2-17x-15 factored is (x-5)(x+1)(x+3)
new problme: (x-5)(x+1)(x+3) / (x-5)

the (x-5) can cancel out

new problem: (x+1)(x+3)
answer: (x+1)(x+3)

Answer 2

The quotient is,
`x^2+4x+3`

Explanation:

Divide:
`(x^3-x^2-17x-15)/(x-5)` using synthetic division.

The steps required for Synthetic division are as follows:

Step 1 : Set up the problem first, set the denominator equal to zero to find the number to put in the division box.

• Once the problem is set up correctly, bring the leading coefficient (i.e first number) straight down.

• Now, multiply the number in the division box with the number you brought down and put the result in the next column.

• Next, add the two numbers together and write the result in the bottom of the row. Repeat the same process, till the end of the problem.

Step 2: Write the final answer. The variables (i.,e x’s) start off one power less than the original denominator and go down one with each term.

Set the denominator equal to 0

i.,e x-5 = 0

⇒ x =5

Using the above steps to find the quotient by using synthetic division as shown below in the attachment.

The quotient we get ;
`x^2+4x+3`