Question

b. $w^4 - 7w^3 - 18w^2 = 0$

Explanation:

Step1: Factor out common term

Factor $w^2$ from the expression:
$w^2(w^2 - 7w - 18) = 0$

Step2: Factor quadratic polynomial

Factor $w^2 - 7w - 18$ into binomials:
$w^2(w - 9)(w + 2) = 0$

Step3: Solve for each factor

Set each factor equal to 0:

1. $w^2 = 0$
2. $w - 9 = 0$
3. $w + 2 = 0$

Step4: Calculate individual solutions

Solve each equation:

1. $w = 0$ (double root)
2. $w = 9$
3. $w = -2$

Answer:

$w = 0$, $w = 9$, $w = -2$