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Q3.

Expert-verifiedFound in: Page 520

Book edition
Student Edition

Author(s)
Carter, Cuevas, Day, Holiday, Luchin

Pages
801 pages

ISBN
9780078884801

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

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

Group terms with common factors from the given polynomial.

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

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

Factor out GCF from each grouping.

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

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

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