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? Step 4: (x2 + 16)(x + 1); Step 5: (x + 4)(x + 4)(x + 1) Step 4: (x2 − 16)(x + 1); Step 5: (x + 4)(x + 4)(x + 1) Step 4: (x2 − 16)(x + 1); Step 5: (x − 4)(x + 4)(x + 1) Step 4: (x2 + 16)(x + 1); Step 5: (x − 4)(x + 4)(x + 1)

Answer 1

`S1:\ x^3-16x+x^2-16\\\\S2:\ x^3+x^2-16x-16\\\\S3:\ x^2(x+1)-16(x+1)\\S4:(x^2-16)(x+1)\\\\S5:\ (x-4)(x+4)(x+1)`

`Used:\\a^2-b^2=(a-b)(a+b)\ \ \ /x^2-16=x^2-4^2/`