You want to write $3x^2 - 2x - 8$ as a product of two binomials, like $(3x + m)(x + n)$. The numbers $m$ and $n$ must multiply to $-8 \times 3$ and add to $-2$.

Once you have factored the quadratic into something like $(\text{expression})_1(\text{expression})_2 = 0$, remember that each factor can be set equal to zero to create simple linear equations to solve for $x$.

After you find the two values of $x$, compare them to each option. Remember that both numbers in the answer choice must satisfy the equation, not just one.

In Desmos, type the equation y = 3x^2 - 2x - 8 to graph the parabola corresponding to the quadratic.

Look for the points where the graph crosses the x-axis (where $y = 0$). Hover over those intersection points or tap them to see their $x$-coordinates; these $x$-values are the solutions to the equation.

Compare the two $x$-values you see on the x-axis with the pairs listed in choices A–D, and select the choice that lists exactly those two values.

The equation is a quadratic in standard form:

Because the coefficients are relatively small integers, it is efficient to try factoring it into the form $(ax + b)(cx + d) = 0$ and then solve each factor for $x$.

We want two numbers that multiply to $3 \times (-8) = -24$ and add to $-2$ (the middle coefficient).

Those numbers are $4$ and $-6$ because $4 + (-6) = -2$ and $4 \times (-6) = -24$.

Rewrite the middle term using $4x$ and $-6x$ and factor by grouping:

Now the quadratic is factored.

If a product is zero, then at least one factor must be zero. So from

we get two simple equations:

• $3x + 4 = 0 \Rightarrow 3x = -4 \Rightarrow x = -\dfrac{4}{3}$
• $x - 2 = 0 \Rightarrow x = 2$

So the solutions to the quadratic are $x = -\dfrac{4}{3}$ and $x = 2$. Among the choices, this pair appears in option B.