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Expanding and factoringAlgebraHigh schoolabout 0:59

Factor x^2 - 3x - 54: animated lesson

A narrated, step-by-step expanding and factoring video lesson with captions. Final answer: (x - 9)(x + 6).

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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 (0.4 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Worked example
$x^{2} - 3x - 54$
2. Step by step
1. $x^{2} - 3x - 54$
  Write the polynomial in standard form
2. $x^{2} - 3x - 54 = 1x^2 + 6x - 9x - 54$
  Use the AC method
3. Factor by grouping
4. $(x - 9)(x + 6)$
  Write the complete factorization
3. The answer
$(x - 9)(x + 6)$
x^2 - 3x - 54 = (x - 9)(x + 6)
4. Check
- Expanding (x - 9)(x + 6) gives back x^2 - 3x - 54.

Transcript

The problem. Here is the problem: x squared minus 3x minus 54. 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 negative 54 equals negative 54. Find two numbers whose product is negative 54 and whose sum is b equals negative 3: 6 and negative 9. Factor by grouping. Group the first two and last two terms, factor each group, then factor out the common binomial. The roots are negative 6 and 9. Write the complete factorization.

The answer. So the answer is (x minus 9)(x plus 6). x squared minus 3x minus 54 factors completely over the rationals as (x minus 9)(x plus 6).

Check. Expanding (x minus 9)(x plus 6) gives back x squared minus 3x minus 54.

About expanding and factoring

Expand products of brackets and factor polynomials completely.

Factor x^2 - 3x - 54: Animated Step-by-Step Lesson