Question

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

Answer 1

x^3 -x + 2x^2 − 2
= x^3 + 2x^2 - x - 2
= x^2(x + 2) - 1(x+2)
= (x + 2)(x^2 - 1)
= (x+2) (x+1)(x-1)

Step 1: x3 − x + 2x2 − 2
Step 2: x3 + 2x2 − x − 2
Step 3: x2(x + 2) − 1(x + 2)
step 4: (x + 2)(x^2 - 1)
step 5: (x+2) (x+1)(x-1)

answer
Step 4: (x^2 − 1)(x + 2); Step 5: (x − 1)(x + 1)(x + 2)

Answer 2

4. (x^2 - 1)(x + 2)

5. (x - 1)(x + 1(x + 2)