Factor the expression. $6 x ^ { 2 } + 13 x + 6$
A) $( 2 x + 3 ) ^ { 2 }$
B) $( x + 3 ) ( 6 x + 2 )$
C) $( 2 x + 1 ) ( 3 x + 6 )$
D) $( 6 x + 1 ) ( x + 6 )$
E) $( 2 x + 3 ) ( 3 x + 2 )$

Question

Quizplus · Accepted Answer

We need to find two binomials that multiply to give us the given trinomial. The first term must be of the form (3x)(2x) = 6x^2. The last term must be of the form (3)(2) = 6. So, we can try (3x + a)(2x + b) where a and b are constants. Multiplying this out gives us:
$$6x^2 + (3a + 2b)x + ab$$
We need to find values of a and b such that (3a + 2b) = 13 and ab = 6.
We can try a = 2 and b = 3, which gives us (3x + 2)(2x + 3) = 6x^2 + 13x + 6. Therefore, the correct choice is E.

Factor the Expression 6x2+13x+66 x ^ { 2 } + 13 x + 66x2+13x+6

Factor the Expression $6 x ^ { 2 } + 13 x + 6$