Question

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

Answer 1

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.

Answer 2

Answer:

step 4

Step-by-step explanation: