Question

Some steps to rewrite the expression x3 - 16x + x2 - 16 as a product of three factors are shown below: Step 1: x3 - 16x + x2 - 16 Step 2: x3 + x2 - 16x - 16 Step 3: x2(x + 1) - 16(x + 1) Which of the following best shows the next two steps to rewrite the expression?

a. Step 4: (x2 + 16)(x + 1); Step 5: (x + 4)(x + 4)(x + 1)
b. Step 4: (x2 - 16)(x + 1); Step 5: (x + 4)(x + 4)(x + 1)
c. Step 4:(x2 - 16)(x + 1); Step 5: (x - 4)(x + 4)(x + 1)
d. Step 4: (x2 + 16)(x + 1); Step 5: (x - 4)(x + 4)(x + 1)

Answer 1

Step 4: Factor out (x+1) expression:
`(x^2-16)(x+1)`

Step 5: Use a^2 - b^2 = (a-b)(a+b) formula to rewrite an expression x^2-16 of factor:
`(x-4)(x+4)(x+1)`

ANSWER: c)

Answer 2

(C)

Explanation:

The given expression is:

`x^3-16x+x^2-16`

Step 1.
`x^3-16x+x^2-16`

Step 2.
`x^3+x^2-16x-16`

Step 3.
`x^2(x+1)-16(x+1)`

Step 4.
`(x^2-16)(x+1)`

Solving
`x^2-16 as (x+4)(x-4)`

Step 5.
`(x+4)(x-4)(x+1)`

which are the required steps to rewrite the given expression as the product of three factors.

Hence, option C is correct.