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

Answer:

(C)

Step-by-step 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.