Question

select the correct answer.
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: Expand Option A

To expand \((5x + 1)(x + 6)\), we use the distributive property (FOIL method):

$$
LATEXBLOCK0
$$

This is not equal to \(5x^{2}+17x + 6\), so Option A is incorrect.

Step2: Expand Option B

Expand \((5x + 2)(x + 3)\) using the FOIL method:

$$
LATEXBLOCK1
$$

This matches the given quadratic expression \(5x^{2}+17x + 6\). But we can check the other options for completeness.

Step3: Expand Option C

Expand \((5x + 3)(x + 2)\):

$$
LATEXBLOCK2
$$

This is not equal to \(5x^{2}+17x + 6\), so Option C is incorrect.

Step4: Expand Option D

Expand \((5x + 6)(x + 1)\):

$$
LATEXBLOCK3
$$

This is not equal to \(5x^{2}+17x + 6\), so Option D is incorrect.

Answer:

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