Solve a problem

Expanding and factoringAlgebraHigh schoolabout 0:40

Factor x^2 + 1: animated lesson

A narrated, step-by-step expanding and factoring video lesson with captions. Final answer: x^2 + 1.

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

Transcript

The problem. Here is the problem: x squared plus 1. Factor a polynomial over the rational numbers.

Step by step. Write the polynomial in standard form. Check the discriminant. b squared minus 4ac equals negative 4. It is negative, so there are no real roots and the quadratic does not factor over the rational numbers. The polynomial is prime over the rationals.

The answer. So the answer is x squared plus 1. x squared plus 1 has no factors with rational coefficients other than constants, so it is already fully factored over the rationals.

Check. Expanding x squared plus 1 gives back x squared plus 1.

About expanding and factoring

Expand products of brackets and factor polynomials completely.

Factor x^2 + 1: Expanding and factoring Step-by-Step Lesson