Question

factor the trinomial, if possible. $40v^{4}+130v^{3}b - 35v^{2}b^{2}$

Explanation:

Step1: Factor out GCF

Identify and factor the greatest common factor (GCF) of all terms. The GCF of $40v^4$, $130v^3b$, and $-35v^2b^2$ is $5v^2$.
$40v^4 + 130v^3b - 35v^2b^2 = 5v^2(8v^2 + 26vb - 7b^2)$

Step2: Factor the quadratic trinomial

Factor $8v^2 + 26vb - 7b^2$ by finding two binomials whose product equals the trinomial. We need two terms that multiply to $8v^2$ and two terms that multiply to $-7b^2$, such that the middle term is $26vb$.
$8v^2 + 26vb - 7b^2 = (4v - b)(2v + 7b)$

Step3: Combine the factors

Substitute the factored quadratic back into the expression from Step1.
$5v^2(4v - b)(2v + 7b)$

Answer:

$5v^2(4v - b)(2v + 7b)$