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Expanding and factoringAlgebraHigh schoolabout 1:05

Factor 16x^2 + 40x + 21: animated lesson

A narrated, step-by-step expanding and factoring video lesson with captions. Final answer: (4x + 3)(4x + 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 (0.4 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Worked example
$16x^{2} + 40x + 21$
2. Step by step
1. $16x^{2} + 40x + 21$
  Write the polynomial in standard form
2. $16x^{2} + 40x + 21 = 16x^2 + 28x + 12x + 21$
  Use the AC method
3. Factor by grouping
4. $(4x + 3)(4x + 7)$
  Write the complete factorization
3. The answer
$(4x + 3)(4x + 7)$
16x^2 + 40x + 21 = (4x + 3)(4x + 7)
4. Check
- Expanding (4x + 3)(4x + 7) gives back 16x^2 + 40x + 21.

Transcript

The problem. Here is the problem: 16x squared plus 40x plus 21. 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 16 times 21 equals 336. Find two numbers whose product is 336 and whose sum is b equals 40: 28 and 12. 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 over 4 and negative 3 over 4. Write the complete factorization.

The answer. So the answer is (4x plus 3)(4x plus 7). 16x squared plus 40x plus 21 factors completely over the rationals as (4x plus 3)(4x plus 7).

Check. Expanding (4x plus 3)(4x plus 7) gives back 16x squared plus 40x plus 21.

About expanding and factoring

Expand products of brackets and factor polynomials completely.

Factor 16x^2 + 40x + 21: Animated Step-by-Step Lesson