Try to write $x^2 - 5x + 6$ in the form $(x-a)(x-b)$. What two integers multiply to $6$ and add up to $-5$?

Once you have the factored form, remember that if a product equals zero, at least one factor must be zero. Solve each simple equation you get and then compare those values to the answer choices.

In Desmos, type y = x^2 - 5x + 6 into an expression line to graph the parabola.

Look for the points where the graph crosses the x-axis (where $y=0$). The x-coordinates of these intercepts are the solutions to the equation $x^2 - 5x + 6 = 0$.

Note the x-values of the intercepts you see on the graph and compare them with the answer choices 1, 2, 4, and 6. The value that matches one of the intercepts is the correct choice.

The equation $x^2 - 5x + 6 = 0$ is a quadratic with leading coefficient 1. A fast way to solve is to factor it into the form $(x-a)(x-b)=0$ and then use the fact that a product is zero only if at least one factor is zero.

To factor $x^2 - 5x + 6$, look for two integers that:

• multiply to $+6$ (the constant term), and
• add to $-5$ (the coefficient of $x$).

The pair $-2$ and $-3$ works because $(-2)\times(-3)=6$ and $-2+(-3)=-5$. So the quadratic can be written as $(x-2)(x-3)=0$.

From $(x-2)(x-3)=0$, the zero product property tells us that either $x-2=0$ or $x-3=0$, so the solutions are $x=2$ and $x=3$. Looking at the answer choices, the only value listed that is a solution is $2$, so the correct answer is $2$ (choice B).