Question 108·Hard·Advanced Math

An identity is true at every input, so you can use several values of $x$. Type $x_1=[1...5]$. Desmos makes the list $[1,2,3,4,5]$ for the next line.

Type the given equation, replacing every $x$ with $x_1$ and $=$ with $\sim$. The $\sim$ tells Desmos to run a regression: find $a$ and $b$ that fit all five inputs. Under PARAMETERS, Desmos shows $a=3$ and $b=4$.

Type $ab$ on a new line. Desmos prints $12$, the product of the two constants. So $ab=12$. Choice B.

No Desmos needed. The $x^2$ coefficient gives the requested product directly. A coefficient is the number multiplying a power of $x$. On the left, only three pairs make an $x^2$ term:

Because the equation is true for all $x$, the two sides must have the same coefficient for each power. The three products give $ab+5$ on the left, so match that with the $17x^2$ term on the right:

Subtract $5$ from both sides:

So the requested product is $12$. Choice B.