Factoring Polynomials
Mathematics
8th - 9th Grade
CCSS covered
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This quiz focuses on factoring polynomials, a fundamental algebraic skill appropriate for grades 8-9. The content systematically covers essential factoring techniques including finding greatest common factors (GCF), factoring quadratic trinomials, factoring by grouping, and polynomial classification. Students need to master several interconnected concepts to succeed: identifying and extracting the GCF from polynomial expressions, recognizing patterns in quadratic expressions that allow factoring into binomial products, understanding the relationship between multiplication and factoring as inverse operations, and applying the distributive property in reverse. The problems require students to work with various polynomial forms, from simple quadratic trinomials like x² + 7x - 30 to more complex expressions requiring multiple steps such as 3x² + 18x + 15, where students must first factor out the GCF before proceeding with further factorization. Students must also understand polynomial terminology and be able to classify expressions by degree and number of terms. This quiz was created by a classroom teacher who designed it for students studying algebra in grades 8-9. The assessment serves multiple instructional purposes and works effectively as a formative evaluation tool to gauge student understanding before moving to more advanced algebraic topics. Teachers can implement this quiz as a warm-up activity to activate prior knowledge, assign it as homework to reinforce classroom instruction, or use it as a review session before unit tests. The variety of question types allows educators to identify specific areas where students struggle, whether with basic GCF extraction, trinomial factoring, or polynomial classification. This quiz aligns with Common Core standards 8.EE.2 and A.SSE.2, which emphasize using properties of integer exponents and rewriting expressions in equivalent forms by factoring. The consistent emphasis on looking for the GCF first reinforces proper mathematical procedure and helps students develop systematic problem-solving approaches that will serve them well in advanced algebra courses.
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12 questions
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1.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
Factor completely. Always look for a GCF first!
3a2 + 4a + 1
Tags
CCSS.HSA.SSE.A.2
CCSS.HSA.APR.A.1
CCSS.HSA.SSE.B.3
2.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
Factor completely. Always look for a GCF first!
2x2 + 6x - 56
Tags
CCSS.HSA.SSE.A.2
CCSS.HSA.APR.A.1
3.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
Factor completely. Always look for a GCF first!
2m² + 3m - 9
Tags
CCSS.HSA.SSE.A.2
CCSS.HSA.APR.A.1
CCSS.HSA.SSE.B.3
4.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
Factor completely. Always look for a GCF first!
x2 + 7x - 30
Tags
CCSS.HSA.SSE.A.2
CCSS.HSA.APR.A.1
CCSS.HSA.SSE.B.3
5.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
Factor completely. Always look for a GCF first!
a2 - a - 12
Tags
CCSS.HSA.SSE.A.2
CCSS.HSA.APR.A.1
CCSS.HSA.SSE.B.3
6.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
What do you call a polynomial that cannot be factored?
Tags
CCSS.HSA.APR.B.2
7.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
Factor completely. Always look for a GCF first!
3x2 + 18x +15
Tags
CCSS.HSA.SSE.A.2
CCSS.HSA.APR.A.1
CCSS.HSA.SSE.B.3
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