Created by George Brown
14 questions
12th Grade
Math
Updated Mar 2026
This Grade 12 mathematics worksheet gives students focused practice solving polynomial equations by factoring. Across 14 items—12 multiple-choice questions and 2 fill-in-the-blank prompts—students solve quadratic and cubic equations, identify zeros from factored functions, determine the number of zeros of a polynomial, and solve equations with fractional roots. The set also reinforces the Zero-Factor Property and the meaning of a repeated solution, with an additional item involving the Quadratic Formula. The worksheet is useful for checking whether students can move from a factored expression to its solutions, factor equations accurately, and record all roots, including negative and fractional values. Multiple-choice items reveal errors in signs, factor pairs, and solution selection, while the fill-in-the-blank items check key vocabulary and learning-target recall. It is a free printable worksheet with a complete answer key for Grade 12 algebra review, independent practice, or an in-class formative assessment.
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WorksheetsAnswer Keyx = -2, x = -3, x = 3
x = 5, x = -4
x = 4, 3
-5/2, 6
This worksheet covers solving quadratic and cubic polynomial equations by factoring, identifying zeros from factored functions, and applying the Zero-Factor Property. Its 12 multiple-choice items require students to find integer and fractional solutions, count polynomial zeros, and recognize solutions from factors, while 2 fill-in-the-blank items check the terms “Zero-Factor Property” and “repeated solution.”
Introduce the Zero-Factor Property by modeling how an equation written as a product equal to zero produces one solution from each factor. Then work through a quadratic and a cubic example before assigning the worksheet, asking students to explain how each factor produces a zero and to check their roots in the original equation. Use the factored-function questions to connect zeros, factors, and x-intercepts conceptually.
Watch for sign errors when students convert factors such as (x + 4) or (2x + 5) into zeros, and for incomplete solution sets when a polynomial has three roots or a repeated solution. Students may also fail to move a constant before factoring, mishandle fractional roots such as 1/4 or -5/2, or confuse the factors with the zeros themselves. The multiple-choice distractors are useful for identifying these specific errors.
This worksheet is available as a printable PDF and as a digital quiz on Wayground, so you can assign the factoring practice in the format that fits your class. It includes a complete answer key for the 14 questions, and printable submissions can be graded by scanning student work with the Wayground for Teachers app. The printable option can also support schools that are reducing screen time.
Use the worksheet’s Advanced Settings to adjust font size and spacing so the algebraic expressions, factor pairs, and multiple-choice options are easier to read. You can also enable a dyslexia-friendly font or translate the worksheet into another language when those changes support access to the factoring practice. These options apply to the worksheet file itself, including its fill-in-the-blank vocabulary items.
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