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Expanding and factoringAlgebraHigh schoolabout 0:56

Factor x^2 + x - 42: animated lesson

A narrated, step-by-step expanding and factoring video lesson with captions. Final answer: (x - 6)(x + 7).

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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 (0.3 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Worked example
$x^{2} + x - 42$
2. Step by step
1. $x^{2} + x - 42$
  Write the polynomial in standard form
2. $x^{2} + x - 42 = 1x^2 + 7x - 6x - 42$
  Use the AC method
3. Factor by grouping
4. $(x - 6)(x + 7)$
  Write the complete factorization
3. The answer
$(x - 6)(x + 7)$
x^2 + x - 42 = (x - 6)(x + 7)
4. Check
- Expanding (x - 6)(x + 7) gives back x^2 + x - 42.

Transcript

The problem. Here is the problem: x squared plus x minus 42. 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 42 equals negative 42. Find two numbers whose product is negative 42 and whose sum is b equals 1: 7 and negative 6. Factor by grouping. Group the first two and last two terms, factor each group, then factor out the common binomial. The roots are negative 7 and 6. Write the complete factorization.

The answer. So the answer is (x minus 6)(x plus 7). x squared plus x minus 42 factors completely over the rationals as (x minus 6)(x plus 7).

Check. Expanding (x minus 6)(x plus 7) gives back x squared plus x minus 42.

About expanding and factoring

Expand products of brackets and factor polynomials completely.

Factor x^2 + x - 42: Expanding and factoring Lesson