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: Expand option A

$(5x + 1)(x + 6) = 5x^2 + 30x + x + 6 = 5x^2 + 31x + 6$ (not match)

Step2: Expand option B

$(5x + 2)(x + 3) = 5x^2 + 15x + 2x + 6 = 5x^2 + 17x + 6$ (matches)

Step3: Verify other options (optional)

Option C: $(5x + 3)(x + 2) = 5x^2 + 10x + 3x + 6 = 5x^2 + 13x + 6$ (not match)
Option D: $(5x + 6)(x + 1) = 5x^2 + 5x + 6x + 6 = 5x^2 + 11x + 6$ (not match)

Answer:

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