Solve a problem

Expanding and factoringAlgebraHigh schoolabout 0:55

Factor x^2 + 13x + 40: animated lesson

A narrated, step-by-step expanding and factoring video lesson with captions. Final answer: (x + 5)(x + 8).

SpeedLanguage

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
$x^{2} + 13x + 40$
2. Step by step
1. $x^{2} + 13x + 40$
  Write the polynomial in standard form
2. $x^{2} + 13x + 40 = 1x^2 + 8x + 5x + 40$
  Use the AC method
3. Factor by grouping
4. $(x + 5)(x + 8)$
  Write the complete factorization
3. The answer
$(x + 5)(x + 8)$
x^2 + 13x + 40 = (x + 5)(x + 8)
4. Check
- Expanding (x + 5)(x + 8) gives back x^2 + 13x + 40.

Transcript

The problem. Here is the problem: x squared plus 13x plus 40. 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 40 equals 40. Find two numbers whose product is 40 and whose sum is b equals 13: 8 and 5. Factor by grouping. Group the first two and last two terms, factor each group, then factor out the common binomial. The roots are negative 8 and negative 5. Write the complete factorization.

The answer. So the answer is (x plus 5)(x plus 8). x squared plus 13x plus 40 factors completely over the rationals as (x plus 5)(x plus 8).

Check. Expanding (x plus 5)(x plus 8) gives back x squared plus 13x plus 40.

About expanding and factoring

Expand products of brackets and factor polynomials completely.

Factor x^2 + 13x + 40: Animated Step-by-Step Lesson