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Expanding and factoringAlgebraHigh schoolabout 1:03

Factor 3x^2 - 15x + 12: animated lesson

A narrated, step-by-step expanding and factoring video lesson with captions. Final answer: 3(x - 4)(x - 1).

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. 1. The problem
    Worked example
    3x2−15x+123x^{2} - 15x + 12
  2. 2. Steps, part 1
    1. 3x2−15x+123x^{2} - 15x + 12
      Write the polynomial in standard form
    2. 3x2−15x+12=3(x2−5x+4)3x^{2} - 15x + 12 = 3\left(x^{2} - 5x + 4\right)
      Factor out the greatest common factor
    3. x2−5x+4=1x2−1x−4x+4x^{2} - 5x + 4 = 1x^2 - 1x - 4x + 4
      Use the AC method
    4. Factor by grouping
  3. 3. Steps, part 2
    1. 3(x−4)(x−1)3(x - 4)(x - 1)
      Write the complete factorization
  4. 4. The answer
    3(x−4)(x−1)3(x - 4)(x - 1)

    3x^2 - 15x + 12 = 3(x - 4)(x - 1)

  5. 5. Check
    • Expanding 3(x - 4)(x - 1) gives back 3x^2 - 15x + 12.

Transcript

The problem. Here is the problem: 3x squared minus 15x plus 12. Factor a polynomial over the rational numbers.

Steps, part 1. Write the polynomial in standard form. Factor out the greatest common factor. Every term is divisible by 3. Use the AC method. Multiply a times c equals 1 times 4 equals 4. Find two numbers whose product is 4 and whose sum is b equals negative 5: negative 1 and negative 4. 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 4.

Steps, part 2. Write the complete factorization.

The answer. So the answer is 3(x minus 4)(x minus 1). 3x squared minus 15x plus 12 factors completely over the rationals as 3(x minus 4)(x minus 1).

Check. Expanding 3(x minus 4)(x minus 1) gives back 3x squared minus 15x plus 12.

About expanding and factoring

Expand products of brackets and factor polynomials completely.

More lessons like this

Factor 3x^2 - 15x + 12: Animated Step-by-Step Lesson