Factor.
-$12 x^{2}+17 x y+6 y^{2}$
A) $(3 x-2 y)(4 x-3 y)$
B) $(12 x+2 y)(x+3 y)$
C) $(3 \mathrm{x}+2 \mathrm{y})(4 \mathrm{x}+3 \mathrm{y})$
D) $(12 x+y)(x+6 y)$

Question

Quizplus · Accepted Answer

The correct factorization of $12 x^{2}+17 x y+6 y^{2}$ is obtained by finding two binomials whose product gives the original trinomial. The coefficients of $x^2$ and $y^2$ terms suggest looking for factors of 12 and 6, respectively, that also work with the middle term when multiplied and added together. The correct combination that gives a middle term of $17xy$ is $3x+2y$ and $4x+3y$, making option C the correct factorization.

Factor - 12x2+17xy+6y212 x^{2}+17 x y+6 y^{2}12x2+17xy+6y2 A) (3x−2y)(4x−3y)(3 x-2 y)(4 x-3 y)(3x−2y)(4x−3y)

Factor
- $12 x^{2}+17 x y+6 y^{2}$ A) $(3 x-2 y)(4 x-3 y)$