Factoring polynomialsEasy
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Factor each one completely. Each has three factors.
1x³ − 3x²
2x³ + 4x² − x − 4
3x³ + 4x² + 5x + 2
4x³ − x
5x³ − x² − 12x
6x³ − 4x² − 4x + 16
Factoring cubic polynomials worksheets
A cubic comes apart one factor at a time: find one root, divide it out, and what is left is a quadratic you already know how to factor. These free printable worksheets ask for the complete factorisation, and the answer key shows which root was found and how.
If they get stuck
Factoring cubic polynomials
The answer key prints on a separate page.
What's on this sheet
Every cubic here starts at x³, so the roots to try are the factors of the constant term and nothing else. For x³ + 4x² + 5x + 2 that is ±1 and ±2 — four candidates, and substituting −1 gives zero. The key writes that search out, because the search is the method: a student who can only factor the cubics they recognise has learned the answers rather than the way to them.
Why this sheet works
Some cubics hand you a factor before any search. x³ − x² − 12x has no constant term, so x comes out of every term and leaves x² − x − 12; x³ − 3x² gives up x² at once. About a third of each sheet starts that way, so that taking out the common factor stays the first thing checked rather than the thing forgotten.
How this one works
x³ − 3x²
x(x² − 3x)
x²(x − 3)
x³ − 3x² = x²(x − 3)
- There is no constant term, so every term carries an x. So x is a factor. What is left is x² − 3x.
- There is no constant term, so every term carries an x. So x is a factor. And the same is true again, so x² comes out altogether.
- Collect the brackets: x³ − 3x² = x²(x − 3). Multiply back out to check.