Question

find the quadratic polynomial that completes the factorization.
$w^3 + 1000 = (w + 10)(square)$

Explanation:

Step1: Recognize sum of cubes

Recall sum of cubes formula: $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$
Here, $w^3 + 1000 = w^3 + 10^3$, so $a=w$, $b=10$.

Step2: Apply the formula

Substitute $a=w$, $b=10$ into the quadratic term:
$a^2 - ab + b^2 = w^2 - (w)(10) + 10^2$

Step3: Simplify the expression

Calculate each term: $w^2 - 10w + 100$

Answer:

$w^2 - 10w + 100$