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Expanding and factoringAlgebraHigh schoolabout 1:01

Factor 4x^2 - 12x - 7: animated lesson

A narrated, step-by-step expanding and factoring video lesson with captions. Final answer: (2x - 7)(2x + 1).

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Transcript

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
$4x^{2} - 12x - 7$
2. Step by step
1. $4x^{2} - 12x - 7$
  Write the polynomial in standard form
2. $4x^{2} - 12x - 7 = 4x^2 + 2x - 14x - 7$
  Use the AC method
3. Factor by grouping
4. $(2x - 7)(2x + 1)$
  Write the complete factorization
3. The answer
$(2x - 7)(2x + 1)$
4x^2 - 12x - 7 = (2x - 7)(2x + 1)
4. Check
- Expanding (2x - 7)(2x + 1) gives back 4x^2 - 12x - 7.

Transcript

The problem. Here is the problem: 4x squared minus 12x minus 7. 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 4 times negative 7 equals negative 28. Find two numbers whose product is negative 28 and whose sum is b equals negative 12: 2 and negative 14. Factor by grouping. Group the first two and last two terms, factor each group, then factor out the common binomial. The roots are negative 1 over 2 and 7 over 2. Write the complete factorization.

The answer. So the answer is (2x minus 7)(2x plus 1). 4x squared minus 12x minus 7 factors completely over the rationals as (2x minus 7)(2x plus 1).

Check. Expanding (2x minus 7)(2x plus 1) gives back 4x squared minus 12x minus 7.

About expanding and factoring

Expand products of brackets and factor polynomials completely.

Factor 4x^2 - 12x - 7: Animated Step-by-Step Lesson