Question

Factor the polynomial $mn+\mathbf{5}m-\mathbf{3}n-\mathbf{15}$.

A$\left(mn-\mathbf{3}\right)\left(5\right)$

B$\left(n-\mathbf{3}\right)\left(m+\mathbf{5}\right)$

C$\left(m-\mathbf{5}\right)\left(n+\mathbf{3}\right)$

D$\left(m-\mathbf{3}\right)\left(n+\mathbf{5}\right)$

Short answer

The factors of given polynomial are $\left(m-\mathbf{3}\right)\left(n+\mathbf{5}\right)$.

Step-by-step solution

Step 1. Group terms with common factors.

Group terms with common factors from the given polynomial.

$\left(mn+5m\right)+\left(-3n-15\right)$

Therefore, the factors of$4x^2+8x+x+2$ are $\left(4x+1\right)\left(x+2\right)$.

Step 2. Factor out GCF.

Factor out GCF from each grouping.

$m\left(n+5\right)-3\left(n+5\right)=\left(m-3\right)\left(n+5\right)$

Step 3. Write the conclusion.

The obtained solution completely matches with option D. Therefore, option D is the required answer.