Question

1. $5b^{3}-42b^{2}+16b$

Explanation:

Step1: Factor out common term

$5b^3 - 42b^2 + 16b = b(5b^2 - 42b + 16)$

Step2: Factor quadratic trinomial

Find two numbers that multiply to $5\times16=80$ and add to $-42$: $-40$ and $-2$. Split the middle term:
$5b^2 - 42b + 16 = 5b^2 - 40b - 2b + 16$
Factor by grouping:
$=5b(b - 8) - 2(b - 8) = (5b - 2)(b - 8)$

Step3: Combine all factors

Substitute factored quadratic back into the expression.

Answer:

$b(5b - 2)(b - 8)$