Use the factoring method to solve the equation. $6 x ^ { 2 } + 11 x + 3 = 0$
A) $- \frac { 3 } { 2 }$ , $- \frac { 1 } { 3 }$
B) $\frac { 1 } { 3 }$ , $\frac { 3 } { 2 }$
C) $- \frac { 1 } { 3 }$ , $\frac { 3 } { 2 }$
D) $- \frac { 3 } { 2 }$ , $\frac { 3 } { 2 }$
E) $- \frac { 3 } { 2 }$ , $\frac { 1 } { 3 }$

Question

Quizplus · Accepted Answer

To solve the quadratic equation $6x^2 + 11x + 3 = 0$ by factoring, we look for two numbers that multiply to $6 \times 3 = 18$ and add to $11$. These numbers are $9$ and $2$. Thus, we can rewrite the equation as $6x^2 + 9x + 2x + 3 = 0$, which factors into $3x(2x + 3) + 1(2x + 3) = 0$, or $(3x + 1)(2x + 3) = 0$. Setting each factor equal to zero gives $x = -\frac{1}{3}$ and $x = -\frac{3}{2}$, respectively.

Use the Factoring Method to Solve the Equation 6x2+11x+3=06 x ^ { 2 } + 11 x + 3 = 06x2+11x+3=0

Use the Factoring Method to Solve the Equation $6 x ^ { 2 } + 11 x + 3 = 0$