Question

b. $r^{5}-r^{4}-42r^{3}=0$

Explanation:

Step1: Factor out common term

Factor $r^3$ from the left side.
$r^3(r^2 - r - 42) = 0$

Step2: Factor quadratic expression

Factor the quadratic $r^2 - r - 42$ into binomials.
$r^3(r - 7)(r + 6) = 0$

Step3: Solve for $r$

Set each factor equal to 0 and solve.
$r^3=0 \implies r=0$; $r-7=0 \implies r=7$; $r+6=0 \implies r=-6$

Answer:

$r = 0$ (multiplicity 3), $r = 7$, $r = -6$