Question

question 36 (1 point)
factor the polynomial completely.
$s^3 - 1$
a $(s - 1)(s^2 - s + 1)$
b $(s - 1)(s^2 + s + 1)$
c $(s - 1)(s^2 + 1)$
d $(s + 1)(s^2 - s + 1)$

Explanation:

Step1: Recall the formula for difference of cubes

The formula for factoring the difference of cubes is \(a^3 - b^3=(a - b)(a^2+ab + b^2)\). Here, \(a = s\) and \(b = 1\) since we have \(s^3-1=s^3 - 1^3\).

Step2: Apply the formula

Substitute \(a = s\) and \(b = 1\) into the difference of cubes formula. We get \((s - 1)(s^2+(s)(1)+1^2)=(s - 1)(s^2 + s+1)\).

Answer:

b. \((s - 1)(s^2 + s + 1)\)