Question

factor the polynomial completely.

1. $x^2 - 15x + 50$
2. $h^3 + 2h^2 - 9h - 18$
3. $-5k^2 - 22k + 15$

Explanation:

Step1: Factor quadratic (Problem 9)

Find two numbers: product 50, sum -15.
$x^2 -15x +50 = (x-5)(x-10)$

Step2: Group cubic terms (Problem10)

Split into two pairs, factor each.
$h^3+2h^2-9h-18 = h^2(h+2)-9(h+2)$

Step3: Factor cubic fully (Problem10)

Factor out common binomial, use difference of squares.
$h^2(h+2)-9(h+2)=(h+2)(h^2-9)=(h+2)(h-3)(h+3)$

Step4: Factor quadratic (Problem11)

Factor out -1, then split middle term.
$-5k^2-22k+15 = -(5k^2+22k-15) = -(5k-3)(k+5)$

Answer:

1. $(x-5)(x-10)$
2. $(h+2)(h-3)(h+3)$
3. $-(5k-3)(k+5)$ or $(-5k+3)(k+5)$