Question

which expression shows the factors of $5x^2 + 17x + 6$?\
a. $(5x + 1)(x + 6)$\
b. $(5x + 2)(x + 3)$\
c. $(5x + 3)(x + 2)$\
d. $(5x + 6)(x + 1)$

Explanation:

Step1: Test Option A via FOIL

$$\begin{align*} (5x + 1)(x + 6) &= 5x\cdot x + 5x\cdot6 + 1\cdot x + 1\cdot6\\ &=5x^2 + 30x + x + 6\\ &=5x^2 + 31x + 6 \end{align*}$$

Step2: Test Option B via FOIL

$$\begin{align*} (5x + 2)(x + 3) &= 5x\cdot x + 5x\cdot3 + 2\cdot x + 2\cdot3\\ &=5x^2 + 15x + 2x + 6\\ &=5x^2 + 17x + 6 \end{align*}$$

Step3: Verify match to target polynomial

The result of Step2 matches $5x^2 + 17x + 6$.

Answer:

B. $(5x + 2)(x + 3)$