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Factor polynomialsTechnique

Technique

Factor polynomials

Pull out the common factor, then match a pattern

3 min 3 steps

Factoring is taking apart what someone multiplied together. I used to take apart pencil sharpeners, so this feels oddly familiar.

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Calls on

Perfect squares, difference of squaresFactExpand squares in full and factor differences fast
Zero-product propertyFactSet each factor to 0, but only when the product is 0

Used by

Rewrite into an equivalent formTacticAim for the choices' form, then check with a number
Solve a nonlinear equationTacticLet the form pick the method, then check every root
Solve a nonlinear systemTacticSubstitute, keep every root, then find each y
Extract features of a quadratic functionTacticPick the form that shows the feature you need
Polynomial zeros, factors, and graphsTacticTurn zeros into factors and factors into graphs
Rational expressionsTechniqueFactor, then cancel factors or share a denominator