Factor an expression

What this page covers

• Taking out a common factor.
• Factoring trinomials, including ones with a leading coefficient other than 1.
• Difference of squares, sum and difference of cubes, and factoring by grouping.
• Not covered here: solving the equation once it is factored (use Solve an equation for x), and expressions that do not factor over the integers, which the page will tell you rather than force.

How to enter the problem

• Type or paste it. x^3 renders as a power; use the math keyboard if you prefer.
• Scan it. Fit the one expression in the frame.
• Choose a photo. Several problems in one photo are solved as a list.
• You can write "Factor" before the expression. Then tap Solve.

Worked example

Common mistakes

• Stopping at $(x - 2)(x^2 - 9)$. "Factor completely" means every factor that can be broken down is broken down.
• Grouping into pairs that do not share a bracket. If the two groups give different brackets, try a different pairing, or the expression does not factor by grouping.
• Sign errors when the second group starts with a minus: $-9x + 18 = -9(x - 2)$, not $-9(x + 2)$.
• For a trinomial like $2x^2 + 7x - 15$, pairing the wrong numbers. You need a pair with product $2 \times (-15) = -30$ and sum 7, which is 10 and $-3$.

Checks, assumptions and limits

• Check by expanding. Multiply the factors back out; you must get the original expression exactly. $(x - 2)(x - 3)(x + 3) = (x - 2)(x^2 - 9) = x^3 - 2x^2 - 9x + 18$.
• Check by roots. Each factor gives a value that makes the original zero: 2, 3 and $-3$ all do.
• Factoring here is over the integers. An expression like $x^2 + 1$ does not factor over the reals; the solver should say so rather than invent factors.
• The order of the factors does not matter.
• HexMath can make mistakes. Double check important steps.

Related tasks

• Solve and work with polynomials
• Simplify an expression
• Solve an equation for x
• Algebra calculator with steps
• Check if a number is prime
• All algebra tasks
• All math tasks