12 questions
9th - 12th Grade
Mathematics
GCF Polynomials is a mathematics worksheet for students in Grades 9–12 who are learning to find the greatest common factor of monomials and polynomial terms, then use that factor to rewrite expressions in factored form. The 12 questions include drag-and-drop, multiple-choice, dropdown, and fill-in-the-blank items involving numerical coefficients and variable factors such as x, m, a, b, and y. Students compare possible common factors, identify the lowest power of each shared variable, select the correct GCF, and complete factorizations such as 6x² − 6x and 4m² + 12mn. The varied response formats provide practice with both recognizing a correct factor and producing missing factors or expressions. This free printable worksheet includes a complete answer key and can support guided practice, independent review, or a check for understanding after instruction on factoring polynomials by their GCF.
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WorksheetsAnswer Key2m²
6x(x - 1)
20x² + 5x
a³b²c³
22b(b² - 1)
8x³y + 5x³y²
100x²
This Grade 9–12 mathematics worksheet helps students find the greatest common factor of monomials and polynomial terms and use it to factor expressions completely. Across 12 drag-and-drop, multiple-choice, dropdown, and fill-in-the-blank items, students compare coefficients and variable exponents, identify the shared factor, and supply the remaining factors.
First model how to find the greatest common numerical factor and the lowest shared power of each variable, then demonstrate dividing every term by that GCF. Use the worksheet’s expressions, such as 6x² − 6x and 4m² + 12mn, to have students explain why the selected factor is common and how multiplying the factored form returns the original expression. Assign the drag-and-drop and multiple-choice items for guided discussion before using the dropdown and fill-in-the-blank items as independent practice.
Watch for students choosing the largest coefficient or highest variable exponent instead of the factor shared by every term, such as selecting 2m³ rather than 2m² for 12m³ and 10m². Students may also stop after identifying the GCF, omit a remaining factor, or distribute it incorrectly when factoring expressions like 22b³ − 22b. Have them verify each completed factorization by multiplying the factors back together.
The worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key for checking the 12 responses. Printable submissions can be graded by scanning student work with the Wayground for Teachers app. The PDF option can also support schools that are reducing screen time while students practise finding GCFs and factoring polynomials.
In the worksheet’s Advanced Settings, adjust font spacing or increase the font size so the algebraic expressions and answer choices are easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language. These options can be used with the drag-and-drop, multiple-choice, dropdown, and fill-in-the-blank factoring items.
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