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Expanding and factoringAlgebraHigh schoolabout 0:57

Factor x^2 + 12x + 27: animated lesson

A narrated, step-by-step expanding and factoring video lesson with captions. Final answer: (x + 3)(x + 9).

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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
$x^{2} + 12x + 27$
2. Step by step
1. $x^{2} + 12x + 27$
  Write the polynomial in standard form
2. $x^{2} + 12x + 27 = 1x^2 + 9x + 3x + 27$
  Use the AC method
3. Factor by grouping
4. $(x + 3)(x + 9)$
  Write the complete factorization
3. The answer
$(x + 3)(x + 9)$
x^2 + 12x + 27 = (x + 3)(x + 9)
4. Check
- Expanding (x + 3)(x + 9) gives back x^2 + 12x + 27.

Transcript

The problem. Here is the problem: x squared plus 12x plus 27. 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 27 equals 27. Find two numbers whose product is 27 and whose sum is b equals 12: 9 and 3. Factor by grouping. Group the first two and last two terms, factor each group, then factor out the common binomial. The roots are negative 9 and negative 3. Write the complete factorization.

The answer. So the answer is (x plus 3)(x plus 9). x squared plus 12x plus 27 factors completely over the rationals as (x plus 3)(x plus 9).

Check. Expanding (x plus 3)(x plus 9) gives back x squared plus 12x plus 27.

About expanding and factoring

Expand products of brackets and factor polynomials completely.

Factor x^2 + 12x + 27: Animated Step-by-Step Lesson