Question

which of the binomials below is a factor of this trinomial?
$3x^2 + 19x + 6$
a. $3x+1$
b. $3x-6$
c. $3x+6$
d. $3x-1$

Explanation:

Step1: Split middle term of trinomial

Find two numbers that multiply to $3\times6=18$ and add to 19: 18 and 1.
Rewrite trinomial: $3x^2 + 18x + x + 6$

Step2: Factor by grouping

Group terms: $(3x^2 + 18x) + (x + 6)$
Factor each group: $3x(x + 6) + 1(x + 6)$
Combine factors: $(3x + 1)(x + 6)$

Step3: Match with given options

Compare the factored form to the choices.

Answer:

A. $3x+1$