Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime.
-$$12 x ^ { 2 } + 23 x + 10$$
A) $( 3 x + 2 ) ( 4 x + 5 )$
B) $( 4 x + 2 ) ( 3 x + 5 )$
C) $( x + 2 ) ( 12 x + 5 )$
D) $( 3 x - 2 ) ( 4 x - 5 )$

Question

Quizplus · Accepted Answer

To factor $12x^2 + 23x + 10$, we look for two numbers that multiply to $12 \times 10 = 120$ and add to $23$. These numbers are $15$ and $8$. Rewriting the middle term: $12x^2 + 15x + 8x + 10$, and factoring by grouping: $3x(4x + 5) + 2(4x + 5)$, we get $(3x + 2)(4x + 5)$.

Factor Completely Using the Grouping Method to Factor Trinomials 12x2+23x+1012 x ^ { 2 } + 23 x + 1012x2+23x+10

Factor Completely Using the Grouping Method to Factor Trinomials $12 x ^ { 2 } + 23 x + 10$