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

Step 1: x3 − 9x + x2 − 9
Step 2: x3 + x2 − 9x − 9
Step 3: x2(x + 1) − 9(x + 1)

Which of the following best shows the next two steps to rewrite the expression?
Step 4: (x2 + 9)(x + 1); Step 5: (x + 3)(x + 3)(x + 1)
Step 4: (x2 − 9)(x + 1); Step 5: (x + 3)(x + 3)(x + 1)
Step 4: (x2 + 9)(x + 1); Step 5: (x − 3)(x + 3)(x + 1)
Step 4: (x2 − 9)(x + 1); Step 5: (x − 3)(x + 3)(x + 1)

Respuesta :

ukichan
the last one
because (x2-9)=(x-3)(x+3)

Answer:

The correct option is D) Step 4:[tex](x^2-9)(x+1)[/tex]; Step 5: (x − 3)(x + 3)(x + 1).

Step-by-step explanation:

Consider the provided expression.

[tex]x^3 - 9x + x^2 - 9[/tex]

Step 1: The provided expression is:

[tex]x^3 - 9x + x^2 - 9[/tex]

Step 2:

[tex]x^3 +x^2- 9x - 9[/tex]

Step 3:

[tex]x^2(x+1)-9(x +1)[/tex]

Step 4:

[tex](x^2-9)(x+1)[/tex]

This can be written s:

[tex](x^2-3^2)(x+1)[/tex]

Step 5: Use the formula, [tex](a^2-b^2)=(a+b)(a-b)[/tex]

[tex](x-3)(x+3)(x+1)[/tex]

Hence, the correct option is D) Step 4: [tex](x^2-9)(x+1)[/tex]; Step 5: (x − 3)(x + 3)(x + 1).

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