Question

Completely factor the given polynomial, if possible. If the polynomial cannot be factored, write NF for your answer.V^2+v-30

Answer 1

The quadratic expression given in the question is

$v^2+v-30$

Concept: To factorize the expression above, we will have to look for two factors that will multiply each other to give -30 and the same factors will add up together to give +1

By try and error, the two factors will be

$\begin{gathered} +6\times-5=-30 \\ +6-5=+1 \end{gathered}$

By replacing the factors in the expression, we will have

$\begin{gathered} v^2+v-30 \\ =v^2+6v-5v-30 \\ =(v^2+6v)-(5v-30) \\ =v(v+6)-5(v+6) \\ =(v+6)(v-5) \end{gathered}$

Hence,

The final answer = (v + 6)(v - 5)