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Expanding and factoringAlgebraHigh schoolabout 1:10

Factor 16x^2 - 44x + 28: animated lesson

A narrated, step-by-step expanding and factoring video lesson with captions. Final answer: 4(4x - 7)(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 (0.5 MB) · Captions (WebVTT)

Steps on screen

  1. 1. The problem
    Worked example
    16x2−44x+2816x^{2} - 44x + 28
  2. 2. Steps, part 1
    1. 16x2−44x+2816x^{2} - 44x + 28
      Write the polynomial in standard form
    2. 16x2−44x+28=4(4x2−11x+7)16x^{2} - 44x + 28 = 4\left(4x^{2} - 11x + 7\right)
      Factor out the greatest common factor
    3. 4x2−11x+7=4x2−4x−7x+74x^{2} - 11x + 7 = 4x^2 - 4x - 7x + 7
      Use the AC method
    4. Factor by grouping
  3. 3. Steps, part 2
    1. 4(4x−7)(x−1)4(4x - 7)(x - 1)
      Write the complete factorization
  4. 4. The answer
    4(4x−7)(x−1)4(4x - 7)(x - 1)

    16x^2 - 44x + 28 = 4(4x - 7)(x - 1)

  5. 5. Check
    • Expanding 4(4x - 7)(x - 1) gives back 16x^2 - 44x + 28.

Transcript

The problem. Here is the problem: 16x squared minus 44x plus 28. 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 4. Use the AC method. Multiply a times c equals 4 times 7 equals 28. Find two numbers whose product is 28 and whose sum is b equals negative 11: negative 4 and negative 7. 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 7 over 4.

Steps, part 2. Write the complete factorization.

The answer. So the answer is 4(4x minus 7)(x minus 1). 16x squared minus 44x plus 28 factors completely over the rationals as 4(4x minus 7)(x minus 1).

Check. Expanding 4(4x minus 7)(x minus 1) gives back 16x squared minus 44x plus 28.

About expanding and factoring

Expand products of brackets and factor polynomials completely.

More lessons like this

Factor 16x^2 - 44x + 28: Animated Step-by-Step Lesson