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Expanding and factoringAlgebraHigh schoolabout 0:54

Factor x^2 - 4x + 3: animated lesson

A narrated, step-by-step expanding and factoring video lesson with captions. Final answer: (x - 3)(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
$x^{2} - 4x + 3$
2. Step by step
1. $x^{2} - 4x + 3$
  Write the polynomial in standard form
2. $x^{2} - 4x + 3 = 1x^2 - 1x - 3x + 3$
  Use the AC method
3. Factor by grouping
4. $(x - 3)(x - 1)$
  Write the complete factorization
3. The answer
$(x - 3)(x - 1)$
x^2 - 4x + 3 = (x - 3)(x - 1)
4. Check
- Expanding (x - 3)(x - 1) gives back x^2 - 4x + 3.

Transcript

The problem. Here is the problem: x squared minus 4x plus 3. Factor a polynomial over the rational numbers.

Step by step. Write the polynomial in standard form. Use the AC method. Multiply a times c equals 1 times 3 equals 3. Find two numbers whose product is 3 and whose sum is b equals negative 4: negative 1 and negative 3. Factor by grouping. Group the first two and last two terms, factor each group, then factor out the common binomial. The roots are 1 and 3. Write the complete factorization.

The answer. So the answer is (x minus 3)(x minus 1). x squared minus 4x plus 3 factors completely over the rationals as (x minus 3)(x minus 1).

Check. Expanding (x minus 3)(x minus 1) gives back x squared minus 4x plus 3.

About expanding and factoring

Expand products of brackets and factor polynomials completely.

Factor x^2 - 4x + 3: Expanding and factoring Lesson