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Factoring

Common factors, difference of squares, trinomials and cubes.

Factoring reverses multiplication. Always take out a common factor first, then look for a pattern: a² − b² = (a − b)(a + b); a² ± 2ab + b² = (a ± b)²; a³ ± b³ = (a ± b)(a² ∓ ab + b²); and for a trinomial, two numbers whose product is a·c and whose sum is b.

Worked example · factor x^2 - 9

Algebra · Factoring

Factor x^2 - 9

x^{2} - 9

Step by step

  1. x^{2} - 9

    Start from the expression.

  2. \left(x - 3\right) \left(x + 3\right)

    Difference of two squares: a² − b² = (a − b)(a + b).

Reveal the answer
\left(x - 3\right) \left(x + 3\right)

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How to: Factoring

  1. Start from the expression.
  2. Difference of two squares: a² − b² = (a − b)(a + b).

Questions people ask

What does it mean to solve an equation?

To find every value of the unknown that makes both sides equal. Each step is an operation applied to both sides that keeps the solution set the same, until the unknown stands alone.

Why do I sometimes get two answers?

A quadratic can cross the axis twice, so it can have two solutions. A degree-n polynomial has up to n. The graph shows where each one comes from.

How do I know whether to factor or use the quadratic formula?

Try factoring for a few seconds: look for two numbers that multiply to a·c and add to b. If nothing obvious appears, the discriminant b² − 4ac tells you how many real roots there are, and the formula finds them without guessing.

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