Question

Some steps to rewrite the expression x3 − 9x + x2 − 9 as a product of three factors are shown below:

Step 1: x^3 − 9x + x^2 − 9
Step 2: x^3 + x^2 − 9x − 9
Step 3: x^2(x + 1) − 9(x + 1)
Which of the following best shows the next two steps to rewrite the expression? (4 points)
Select one:
a. Step 4: (x^2 + 9)(x + 1); Step 5: (x + 3)(x + 3)(x + 1)
b. Step 4: (x^2 − 9)(x + 1); Step 5: (x + 3)(x + 3)(x + 1)
c. Step 4: (x^2 + 9)(x + 1); Step 5: (x − 3)(x + 3)(x + 1)
d. Step 4: (x^2 − 9)(x + 1); Step 5: (x − 3)(x + 3)(x + 1)

Answer 1

step 4

Explanation:

Answer 2

Answer: The correct option is (d)
`\textup{Step 4: }(x^2-9)(x+1);~\textup{Step 5: }(x-3)(x+3)(x+1).`

Step-by-step explanation: The given steps in rewriting the expression
`x^3-9x+x^2-9` as a product of three factors are as follows:

`\textup{Step 1: }x^3-9x+x^2-9\\\\\textup{Step 2: }x^3+x^2-9x-9\\\\\textup{Step 3: }x^2(x+1)-9(x+1).`

We are given to select the correct option that shows the next two steps to rewrite the expression.

We can factor the given expression as follows:

`x^3-9x+x^2-9\\\\=x^3+x^2-9x-9\\\\=x^2(x+1)-9(x+1)\\\\=(x^2-9)(x+1)~~~~~~~~~~~\textup{[Step 4]}\\\\=(x-3)(x+3)(x+1).~~~~~~~\textup{[Step 5]}`

Therefore, the next two steps are

`\textup{Step 4: }(x^2-9)(x+1);~\textup{Step 5: }(x-3)(x+3)(x+1).`

Thus, option (d) is corect.