Question: Factor the trinomial. $v^2 + 5v - 36$ Select the correct choice below and, if necessary, fill in…

Factor the trinomial.

$v^2 + 5v - 36$

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. $v^2 + 5v - 36 = \boxed{\quad}$ (Factor completely.)

B. The polynomial is prime.

Solution

To factor the trinomial \( v^2 + 5v - 36 \), we need to find two numbers that multiply to \(-36\) and add to \(5\). First, list the factor pairs of \(-36\): - \((1, -36)\), \((-1, 36)\), \((2, -18)\), \((-2, 18)\), \((3, -12)\), \((-3, 12)\), \((4, -9)\), \((-4, 9)\), \((6, -6)\) Next, identify the pair that adds to \(5\): - \((-4, 9)\) This means we can factor the trinomial as: \[ (v - 4)(v + 9) \] So, the trinomial \( v^2 + 5v - 36 \) factors to: \[ v^2 + 5v - 36 = (v - 4)(v + 9) \]