Once you know the greatest common factor, write $35x$ and $21$ as that number times something else (for example, $35x = \text{GCF} \times \text{something}$).

After you factor, multiply back out (distribute) to make sure you get $35x - 21$ again. Only the correct option will distribute back to the original expression.

In Desmos, type f(x) = 35x - 21 to represent the original expression.

Type functions for each option, for example: g(x) = 5(7x - 4), h(x) = 7(5x + 3), p(x) = 3(12x - 7), and q(x) = 7(5x - 3).

Click the gear icon next to each function and enable a table, or use the + button to add a table. Plug in several $x$-values (like $x = 0, 1, 2, -1$) and see which option’s $y$-values always match the $y$-values of $f(x) = 35x - 21$. The function that matches for all tested values corresponds to the equivalent expression.

Look at the coefficients $35$ and $21$. Both are divisible by $7$:

• $35 = 7 \times 5$
• $21 = 7 \times 3$

So the greatest common factor of $35x$ and $21$ is $7$.

Rewrite each term by showing the factor of $7$:

Because each term has a factor of $7$, the expression equals $7$ times a binomial. We will write that binomial and select the matching answer in the next step.

Factor out $7$ from both terms:

Compare with the answer choices: this matches choice D, $7(5x - 3)$.