Question

question 11
factor the following problem completely. first factor out the greatest common factor, and then factor the remaining trinomial.
$r^4 - 1r^3 - 6r^2$
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question 12
factor the following trinomial.
$y^2 - 3yb - 18b^2$

Explanation:

Step1: Factor out GCF of $r^4 - r^3 -6r^2$

$\text{GCF}(r^4, r^3, 6r^2) = r^2$, so:
$r^4 - r^3 -6r^2 = r^2(r^2 - r - 6)$

Step2: Factor the trinomial $r^2 - r -6$

Find two numbers that multiply to $-6$ and add to $-1$: $-3$ and $2$.
$r^2 - r -6 = (r - 3)(r + 2)$

Step3: Combine factors for first expression

$r^4 - r^3 -6r^2 = r^2(r - 3)(r + 2)$

Step4: Factor trinomial $y^2 - 3yb -18b^2$

Find two numbers that multiply to $-18b^2$ and add to $-3b$: $-6b$ and $3b$.
$y^2 - 3yb -18b^2 = (y - 6b)(y + 3b)$

Answer:

1. $r^2(r - 3)(r + 2)$
2. $(y - 6b)(y + 3b)$