Question 943·Medium·Math

Type $y=3x^2-2x-8$ and $y=0$, one per line. Click both crossings. Desmos labels them near $(-1.333,0)$ and $(2,0)$. Each crossing’s $x$-coordinate solves the equation, because the expression equals $0$ there. The negative coordinate is rounded, so don’t treat $-1.333$ as exact.

The negative crossing is near $-1.333$, so test the nearby fraction $-\frac43$ from the choices. Type $3(-\frac43)^2-2(-\frac43)-8$. Desmos prints $0$, confirming that fraction exactly; the other crossing gives $x=2$. All solutions are $-\frac43$ and $2$. Choice B.

For factoring by grouping, multiply the first coefficient $3$ by the constant $-8$ to get $-24$. Find two numbers that multiply to $-24$ and add to the middle coefficient $-2$: $4$ and $-6$. Rewrite $-2x$ as $4x-6x$:

Factor each pair of terms:

Take out the shared factor $3x+4$:

The zero-product property says that if two factors multiply to $0$, at least one is $0$. Set each factor to $0$:

Add $2$ to the first equation:

Subtract $4$ from the second:

Divide by $3$:

The solutions are $-\frac43$ and $2$. Choice B.