Question

find the quadratic polynomial that completes the factorization.
$u^3 - 1 = (u - 1)(square)$

Explanation:

Step1: Recall difference of cubes formula

The difference of cubes formula is $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$.

Step2: Identify a and b

Here, $a = u$ and $b = 1$ (since $1 = 1^3$).

Step3: Substitute into the formula

Substitute $a = u$ and $b = 1$ into $a^2 + ab + b^2$: $u^2 + (u)(1) + 1^2 = u^2 + u + 1$.

Answer:

$u^2 + u + 1$