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

so.... what do you think?

Answer 2

how about taking common factor? \(\bf x^2\color{blue}{(x + 1)} - 16\color{blue}{(x + 1)}\) do you see any we can use?

Answer 3

I couldnt decide between B and C @jdoe0001

Answer 4

well. what would be YOUR next step ?

Answer 5

I know how to do step 4, but i forgot how to do step 5 ): @jdoe0001

Answer 6

ok.... well, let's take one STEP at a time =)...

what would be step 4?

Answer 7

the answer for step 4 is (6^2-16)(x+1)

Answer 8

@jdoe0001

Answer 9

@jdoe0001

Answer 10

ohh yes, that'd be step number 4, sorry I got a bit caught up

Answer 11

its okay (: what do i do next?

Answer 12

\(\bf x^2(x+1)-16(x+1)\implies (x^2-16)(x+1)\\ \quad \\
\textit{recall that }\qquad a^2-b^2 = (a-b)(a+b)\qquad thus\\ \quad \\
(x^2-16)(x+1)\implies (x^2-4^2)(x+1)\implies (x-4)(x+4)(x+1)\)

Answer 13

THANK YOU THANK YOU THANK YOU!!!

Answer 14

yw