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Expanding and factoringAlgebraHigh schoolabout 0:42

Factor x^3 - x: animated lesson

A narrated, step-by-step expanding and factoring video lesson with captions. Final answer: x(x - 1)(x + 1).

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Video with a synthetic English voice and captions. Pick another language for subtitles in that language, or open the interactive version.

Video narrated by a synthetic voice (Piper TTS, en_US-ljspeech-high voice (LJ Speech dataset, public domain)); the steps come from our maths engine and the answer was checked independently. Download MP4 (0.3 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Worked example
$x^{3} - x$
2. Step by step
1. $x^{3} - x$
  Write the polynomial in standard form
2. $x^{3} - x = x\left(x^{2} - 1\right)$
  Factor out the greatest common factor
3. Recognise a special pattern
4. $x(x - 1)(x + 1)$
  Write the complete factorization
3. The answer
$x(x - 1)(x + 1)$
x^3 - x = x(x - 1)(x + 1)
4. Check
- Expanding x(x - 1)(x + 1) gives back x^3 - x.

Transcript

The problem. Here is the problem: x cubed minus x. Factor a polynomial over the rational numbers.

Step by step. Write the polynomial in standard form. Factor out the greatest common factor. Every term is divisible by x. Recognise a special pattern. The remaining factor is a difference of squares: a squared minus b squared equals (a minus b)(a plus b). Write the complete factorization.

The answer. So the answer is x(x minus 1)(x plus 1). x cubed minus x factors completely over the rationals as x(x minus 1)(x plus 1).

Check. Expanding x(x minus 1)(x plus 1) gives back x cubed minus x.

About expanding and factoring

Expand products of brackets and factor polynomials completely.

Factor x^3 - x: Expanding and factoring Step-by-Step Lesson