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How to Check Your Factoring in Desmos

Last updated: October 9, 2026

Type the original expression on one row of Desmos and your factored version on the next. If you factored it correctly, the two graphs land exactly on top of each other and you see one curve. If you got it wrong, you see two separate curves, and they only meet at the inputs where your mistake happens to cancel out.

The problem

Solve: x² − 3x − 4 = 0
Solution: x = −1 and x = 4

Factor the left side and you get (x + 1)(x − 4) = 0. Desmos can confirm that factoring before you trust the solutions that come from it.

What do you type?

Two rows:

Row 1: x^2 − 3x − 4
Row 2: (x + 1)(x − 4)

You don't need y = in front. Desmos graphs an expression in x on its own. Both rows draw the same upward parabola in the same place, so the screen shows one curve in two colors stacked on top of each other.

Click the parabola and gray dots appear on the x-axis at (−1, 0) and (4, 0). Those are the solutions, and they match the factors: x + 1 is zero at −1, and x − 4 is zero at 4.

How do you know they really overlap?

Two curves in nearly the same spot can look like one. Click the colored circle beside Row 2 to hide it. If the curve on screen doesn't move, Row 1 was underneath the whole time, and the two expressions are equivalent.

Then zoom out once. Two different expressions can run close together near the origin and split apart further out. If they're equivalent, they stay as one curve at every zoom level.

What does a wrong factoring look like?

Say you flip the signs and write (x − 1)(x + 4). Type it on Row 2.

Now there are two parabolas. They cross once, at (0, −4), and separate everywhere else. That single crossing is the trap. If you had checked your factoring by plugging in x = 0, both sides give −4 and the wrong answer passes. The graph checks every input at once.

Clicking the new curve's x-intercepts also shows you what went wrong. They sit at 1 and −4, which are the right numbers with the signs flipped.

How do you answer "which expression is equivalent"?

When the question gives you answer choices instead of asking you to factor, the method is the same, with more rows:

1. Type the expression from the question on Row 1
2. Type each answer choice on its own row, exactly as printed
3. Hide the choices one at a time. The one that leaves no visible change to Row 1's curve is the answer

If the question uses a letter other than x, like a or t, change it to x on every row. Desmos treats any other letter as a constant and offers you a slider instead of a graph.

The algebra behind the choices, which is factoring patterns, exponent rules and cancelling, is in SAT Equivalent Expressions. This post only covers the check.

What if the question hides a constant?

"If (x + 1)(x + k) = x² − 3x − 4 for all values of x, what is k?"

Type x^2 − 3x − 4 on Row 1 and (x + 1)(x + k) on Row 2. Desmos offers a slider for k. Click it and drag. The second parabola slides around until, at one value, it snaps onto the first and the two colors become one curve. That happens at k = −4.

"For all values of x" is the condition the overlap checks. One crossing isn't enough. The curves have to match everywhere.

If the slider skips past the value, click the number next to k and type each answer choice in turn.

How do you practice this?

Pick 10 equivalent-expression or factoring questions from practice tests. For each one:

1. Work it by hand first, without Desmos
2. Type the original and your answer on two rows, then hide your row to confirm the overlap
3. When the curves split, click the x-intercepts of your version and compare them to the original's to see which sign or factor you got wrong

The goal is a hand method you trust and a 20-second check behind it for the questions where one sign error costs the point.

HIROSCORE tracks equivalent expressions as its own skill inside Advanced Math, so a sign-error habit in factoring shows up in your results instead of hiding inside a decent math score. The GPS for your SAT score.