Equations practice
Solve ten factorable quadratic equations with complete exact root sets. Choose factored form, expanded form, rearrangement practice or a balanced mixed sheet.
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Rearrange to zero when needed, factor the quadratic and solve each linear factor. Give all distinct values of the variable.
Download the practice pages alone, or include a separate answer key or teacher model. Longer activities may use more than one page.
Customize this worksheetEasy questions begin as a product of two linear factors equal to zero. Medium questions begin expanded. Hard questions place a nonzero constant on the right, so the equation must first be rearranged to zero. Mixed sheets include all three forms.
Each worksheet includes signed roots, a zero root, a repeated root and a noninteger rational root. The key writes repeated roots once and shows the factoring step for expanded and rearrangement questions.
Learning objective
Use the zero-product property to find every rational root of a factorable quadratic equation.
Worked example
x = −3 or x = −1/2.
Factor as (2x + 1)(x + 3) = 0. Set each factor equal to zero. The two exact roots are −1/2 and −3.
Teaching notes
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Every sheet includes zero, repeated and noninteger rational roots. Mixed practice contains four factored, three expanded and three rearrangement equations.
A useful next step
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