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Ch.4 (4.1-4.4) Big Ideas Quiz

Authored by Kim Brakmeier

Mathematics

9th - 12th Grade

CCSS covered

Used 23+ times

Ch.4 (4.1-4.4) Big Ideas Quiz
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This quiz covers polynomial operations and functions, specifically focusing on factoring, solving, and analyzing polynomial behavior. The questions assess high school Algebra 2 concepts at approximately grades 9-12 level. Students need mastery of factoring techniques including greatest common factor, quadratic factoring, difference of squares, and factoring by grouping. They must understand polynomial division using long division and synthetic division methods, solve quadratic equations by factoring, identify zeros of polynomial functions, and analyze polynomial graphs to determine degree, leading coefficient behavior, and multiplicities. The mathematical reasoning required includes recognizing factoring patterns, applying the zero product property, understanding the relationship between factored form and zeros, and interpreting graphical features like end behavior and turning points. Created by Kim Brakmeier, a Mathematics teacher in US who teaches grade 9-12. This assessment serves as an excellent review tool for polynomial concepts covered in sections 4.1-4.4 of an Algebra 2 curriculum. Teachers can use this quiz for formative assessment to gauge student understanding before a unit test, as a warm-up activity to review previously learned concepts, or as homework to reinforce classroom instruction. The varied question types—from computational factoring problems to graphical analysis—provide comprehensive coverage that helps students make connections between algebraic manipulation and function behavior. This quiz aligns with Common Core standards A-APR.2 (polynomial division), A-APR.3 (polynomial zeros), and F-IF.7c (graphing polynomial functions), supporting student mastery of essential polynomial concepts through multiple representations and problem-solving approaches.

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17 questions

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1.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Solve for n by factoring 2n2+4n16=02n^2+4n-16=0 

-4, 2

-2, 4

-16

-4

Tags

CCSS.HSA-REI.B.4B

2.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Factor completely  x3+3x2+2xx^3+3x^2+2x  

 x(x2+3x+2)x\left(x^2+3x+2\right)  

 x(x2)(x1)x\left(x-2\right)\left(x-1\right)  

 (x+2)(x+1)\left(x+2\right)\left(x+1\right)  

 x(x+2)(x+1)x\left(x+2\right)\left(x+1\right)  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

3.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Factor completely and determine the zeros  4x2814x^2-81  

 (2x9)(2x9); x=92\left(2x-9\right)\left(2x-9\right);\ x=\frac{9}{2}  

 (2x+9)(2x+9); x=92\left(2x+9\right)\left(2x+9\right);\ x=-\frac{9}{2}  

 (2x9)(2x+9); x=±92\left(2x-9\right)\left(2x+9\right);\ x=\pm\frac{9}{2}  

 (x9)(x+9); x=±9\left(x-9\right)\left(x+9\right);\ x=\pm9  

Tags

CCSS.HSA.APR.C.4

4.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Factor completely  3x3+5x29x15\ 3x^3+5x^2-9x-15  

 (x23)(3x+5)\left(x^2-3\right)\left(3x+5\right)  

 (3x3+5x2)(9x15)\left(3x^3+5x^2\right)\left(-9x-15\right)  

 (x23)(3x5)\left(x^2-3\right)\left(-3x-5\right)  

 (x2+3)(3x+5)\left(x^2+3\right)\left(3x+5\right)  

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.APR.B.2

CCSS.HSA.SSE.A.2

5.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

 Divide (2n4+9n334n2+14n+49)÷(n+7)\left(2n^4+9n^3-34n^2+14n+49\right)\div\left(n+7\right) 

 2n45n3+1n2+7n2n^4-5n^3+1n^2+7n  

 2n35n2+n+72n^3-5n^2+n+7  

 2n25n+1+7n+72n^2-5n+1+\frac{7}{n+7}  

 2n25n+1+7x72n^2-5n+1+\frac{7}{x-7}  

Tags

CCSS.HSA.APR.D.6

6.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Divide (x3103x+30)÷(x10)\left(x^3-103x+30\right)\div\left(x-10\right)  

 x3+10x23xx^3+10x^2-3x  

 x2103x^2-103  

 x2+10x3x^2+10x-3  

 x2+10x3x10x^2+10x-\frac{3}{x-10}  

Tags

CCSS.HSA.APR.D.6

7.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Divide (k3+14k2+51k+24)÷(k+5)\left(k^3+14k^2+51k+24\right)\div\left(k+5\right)  

 k2+9k+66k+5k^2+9k+6-\frac{6}{k+5}  

 k2+9k+6+6k+5k^2+9k+6+\frac{6}{k+5}  

 k2+9k+66k5k^2+9k+6-\frac{6}{k-5}  

 k3+9k2+6k6k^3+9k^2+6k-6  

Tags

CCSS.HSA.APR.D.6

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