Skip to content
MathSolver Pro
  • Open the math solver
  • Ask the AI tutor
  • Find an AP course
  • Create a quiz
  • Open the calculator
  • Graphing Calculator
  • Browse all calculators
  • Read math guides
↑ ↓Enter to open · Esc to close
Solve a problem
Expanding and factoringAlgebraHigh schoolabout 1:07

Factor x^3 + 2x^2 - x - 2: animated lesson

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

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. 1. The problem
    Worked example
    x3+2x2−x−2x^{3} + 2x^{2} - x - 2
  2. 2. Steps, part 1
    1. x3+2x2−x−2x^{3} + 2x^{2} - x - 2
      Write the polynomial in standard form
    2. Apply the Rational Root Theorem
    3. x3+2x2−x−2=(x+2)(x2−1)x^{3} + 2x^{2} - x - 2 = (x + 2)\left(x^{2} - 1\right)
      Divide by (x + 2) using synthetic division at x = -2
    4. x2−1=(x+1)(x−1)x^{2} - 1 = (x + 1)\left(x - 1\right)
      Divide by (x + 1) using synthetic division at x = -1
  3. 3. Steps, part 2
    1. x−1=(x−1)(1)x - 1 = (x - 1)\left(1\right)
      Divide by (x - 1) using synthetic division at x = 1
    2. (x−1)(x+1)(x+2)(x - 1)(x + 1)(x + 2)
      Write the complete factorization
  4. 4. The answer
    (x−1)(x+1)(x+2)(x - 1)(x + 1)(x + 2)

    x^3 + 2x^2 - x - 2 = (x - 1)(x + 1)(x + 2)

  5. 5. Check
    • Expanding (x - 1)(x + 1)(x + 2) gives back x^3 + 2x^2 - x - 2.

Transcript

The problem. Here is the problem: x cubed plus 2x squared minus x minus 2. Factor a polynomial over the rational numbers.

Steps, part 1. Write the polynomial in standard form. Apply the Rational Root Theorem. Any rational root p/q has p dividing the constant term negative 2 and q dividing the leading coefficient 1. Testing these candidates gives the roots negative 2, negative 1, 1. Divide by (x plus 2) using synthetic division at x equals negative 2. Divide by (x plus 1) using synthetic division at x equals negative 1.

Steps, part 2. Divide by (x minus 1) using synthetic division at x equals 1. Write the complete factorization.

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

Check. Expanding (x minus 1)(x plus 1)(x plus 2) gives back x cubed plus 2x squared minus x minus 2.

About expanding and factoring

Expand products of brackets and factor polynomials completely.

More lessons like this

Factor x^3 + 2x^2 - x - 2: Animated Step-by-Step Lesson