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Expanding and factoringAlgebraHigh schoolabout 0:41

Factor x^2 - 2: animated lesson

A narrated, step-by-step expanding and factoring video lesson with captions. Final answer: x^2 - 2.

SpeedLanguage

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 (0.2 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Worked example
$x^{2} - 2$
2. Step by step
1. $x^{2} - 2$
  Write the polynomial in standard form
2. Check the discriminant
3. $x^{2} - 2$
  The polynomial is prime over the rationals
3. The answer
$x^{2} - 2$
x^2 - 2 = x^2 - 2
4. Check
- Expanding x^2 - 2 gives back x^2 - 2.

Transcript

The problem. Here is the problem: x squared minus 2. Factor a polynomial over the rational numbers.

Step by step. Write the polynomial in standard form. Check the discriminant. b squared minus 4ac equals 8. It is not a perfect square, so the quadratic does not factor over the rational numbers. The polynomial is prime over the rationals.

The answer. So the answer is x squared minus 2. x squared minus 2 has no factors with rational coefficients other than constants, so it is already fully factored over the rationals.

Check. Expanding x squared minus 2 gives back x squared minus 2.

About expanding and factoring

Expand products of brackets and factor polynomials completely.

Factor x^2 - 2: Expanding and factoring Step-by-Step Lesson