Find the greatest common factor of $7$, $14$, and $21$, and also the highest power of $y$ that divides every term.

After deciding on the common factor, divide each term by it to see what goes inside the parentheses, then compare with the answer choices.

In Desmos, type f(x) = 7x^4 + 14x^3 - 21x^2. (Using $x$ instead of $y$ is fine; we just care about the shape and values.)

Type each choice with $x$ in place of $y$, for example: g(x) = 7x^2(x^2 + 2x - 3), h(x) = 7x^2(x^2 + 2x + 3), etc. Make sure each option is entered correctly.

Look at the graphs: the correct option will have a graph that lies exactly on top of the graph of $f(x)$ for all $x$. You can also tap on a few $x$-values and compare the $y$-values in a table; the equivalent expression is the one that always matches $f(x)$.

Look at the coefficients and the powers of $y$ in each term of $7y^4 + 14y^3 - 21y^2$.

• Coefficients: $7$, $14$, and $21$ all have a greatest common factor of $7$.
• Variables: $y^4$, $y^3$, and $y^2$ all share at least $y^2$ (the smallest exponent among them is $2$).

So the greatest common factor of the whole expression is $7y^2$.

Now divide each term by $7y^2$ to see what will remain inside the parentheses.

• $7y^4 \div 7y^2 = y^2$
• $14y^3 \div 7y^2 = 2y$
• $-21y^2 \div 7y^2 = -3$

So, after factoring out $7y^2$, the expression inside the parentheses will be $y^2 + 2y - 3$.

Put the GCF in front and the result from step 2 in parentheses:

Now compare this factored form to the answer choices. It matches choice A) $7y^2(y^2 + 2y - 3)$, which is the correct answer.