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Expanding and factoringAlgebraHigh schoolabout 0:49

Factor 12x^3 - 3x: animated lesson

A narrated, step-by-step expanding and factoring video lesson with captions. Final answer: 3x(2x - 1)(2x + 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
$12x^{3} - 3x$
2. Step by step
1. $12x^{3} - 3x$
  Write the polynomial in standard form
2. $12x^{3} - 3x = 3x\left(4x^{2} - 1\right)$
  Factor out the greatest common factor
3. Recognise a special pattern
4. $3x(2x - 1)(2x + 1)$
  Write the complete factorization
3. The answer
$3x(2x - 1)(2x + 1)$
12x^3 - 3x = 3x(2x - 1)(2x + 1)
4. Check
- Expanding 3x(2x - 1)(2x + 1) gives back 12x^3 - 3x.

Transcript

The problem. Here is the problem: 12x cubed minus 3x. 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 3x. 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 3x(2x minus 1)(2x plus 1). 12x cubed minus 3x factors completely over the rationals as 3x(2x minus 1)(2x plus 1).

Check. Expanding 3x(2x minus 1)(2x plus 1) gives back 12x cubed minus 3x.

About expanding and factoring

Expand products of brackets and factor polynomials completely.

Factor 12x^3 - 3x: Animated Step-by-Step Lesson 10