Question

factor the trinomial.

\\11u^3v - 30u^2v^2 + 16uv^3 = \\

Explanation:

Identify and extract the greatest common factor

$$ \text{GCF}(11u^3v, -30u^2v^2, 16uv^3) = uv $$

$$ 11u^3v - 30u^2v^2 + 16uv^3 = uv(11u^2 - 30uv + 16v^2) $$

Factor the remaining quadratic trinomial

$$ 11 \times 16 = 176 $$

$$ -8 \times (-22) = 176,\quad -8 + (-22) = -30 $$

$$ 11u^2 - 22uv - 8uv + 16v^2 = 11u(u - 2v) - 8v(u - 2v) = (11u - 8v)(u - 2v) $$

Combine all factored components

$$ uv(11u - 8v)(u - 2v) $$

Answer:

Factor the trinomial.
\(11u^3v - 30u^2v^2 + 16uv^3 =\) <blank>\(uv(11u - 8v)(u - 2v)\)</blank>