First, multiply $3x$ by each term in $2x^2 + x - 4$. Then, separately, multiply $-5$ by each term in $2x^2 + x - 4$.

After you have all the individual products, group together the $x^3$ terms, the $x^2$ terms, the $x$ terms, and the constants. Pay close attention to the signs when you add the coefficients.

Look specifically at the constant that comes from multiplying the constant terms in each binomial/trinomial. What is $(-5) \cdot (-4)$?

In Desmos, type f(x) = (3x - 5)(2x^2 + x - 4) on one line.

On new lines, type:

• A(x) = 6x^3 + 13x^2 - 7x - 20
• B(x) = 6x^3 - 7x^2 - 17x - 20
• C(x) = 6x^3 - 13x^2 + 17x + 20
• D(x) = 6x^3 - 7x^2 - 17x + 20

Click the gear icon next to one function and add a table; Desmos will create an $x$ column and $y$-values for that function. Do the same for the others, then choose a convenient $x$ (like $x = 1$ or $x = 2$) and compare the $y$-values. The choice whose function has the same $y$-value as $f(x)$ for that $x$ is the equivalent expression.

Multiply $3x$ by each term in $2x^2 + x - 4$:

So this part becomes:

Now multiply $-5$ by each term in $2x^2 + x - 4$:

So this part becomes:

Add the results from the two distributions:

Group like terms (same power of $x$):

• Cubic: $6x^3$
• Quadratic: $3x^2 - 10x^2$
• Linear: $-12x - 5x$
• Constant: $20$

Simplify the coefficients:

So the product $(3x - 5)(2x^2 + x - 4)$ is equivalent to $6x^3 - 7x^2 - 17x + 20$, which is choice D.