Finding Zeros of Polynomial Functions
Authored by Kathleen Shaw
Mathematics
10th - 12th Grade
CCSS covered
Used 81+ times
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About
This quiz focuses on polynomial functions, specifically targeting the identification and analysis of zeros, roots, and x-intercepts of polynomial equations ranging from quadratic to quintic degree. The content is appropriate for grades 10-12, as it requires mastery of advanced algebraic concepts including the Factor Theorem, Rational Root Theorem, synthetic division, and complex number operations. Students must demonstrate proficiency in multiple interconnected skills: factoring polynomials when given one factor, applying the relationship between factors and zeros, using the Rational Root Theorem to identify possible rational zeros, performing polynomial division, working with complex conjugate pairs, and analyzing end behavior of polynomial graphs. The quiz also assesses understanding of function composition and the ability to construct polynomials from given zeros, requiring students to work fluidly between algebraic and graphical representations of polynomial behavior. Created by Kathleen Shaw, a Mathematics teacher in US who teaches grade 10-12. This comprehensive assessment serves multiple instructional purposes, functioning effectively as a unit review, formative assessment tool, or homework assignment to reinforce polynomial concepts before summative evaluation. The quiz structure allows teachers to identify specific areas where students need additional support, whether in computational skills like polynomial division or conceptual understanding of the connection between algebraic factors and graphical zeros. Teachers can use individual questions as warm-up problems to activate prior knowledge or assign the entire quiz as practice before standardized assessments. The content aligns with Common Core standards A-APR.2 (knowing and applying the Remainder Theorem), A-APR.3 (identifying zeros of polynomials and using them to construct rough graphs), and F-IF.7c (graphing polynomial functions and identifying key features), making it valuable for supporting curriculum standards while building students' confidence with complex polynomial manipulations.
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21 questions
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1.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
Find all zeros. One zero has been given.
f(x) = x4 + 8x3 + 14x2 - 8x - 15; x = -5
Tags
CCSS.HSA.APR.B.2
CCSS.HSA.APR.B.3
2.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
If the binomial (x - 7) is a factor of the polynomial function f(x), which statement must be true?
Tags
CCSS.HSA.APR.B.2
3.
MULTIPLE CHOICE QUESTION
15 mins • 1 pt
Factor f(x)= x3 - 2x2-13x - 10 given that (x - 5) is one factor.
Tags
CCSS.HSA.APR.B.2
4.
MULTIPLE CHOICE QUESTION
15 mins • 1 pt
Find all the roots of y=x3-2x2+4x-8 (Hint: Factor)
Tags
CCSS.HSF-IF.C.7C
5.
MULTIPLE CHOICE QUESTION
15 mins • 1 pt
Factor:
x3-12x2+47x-60=0 when 5 is a root.
Tags
CCSS.HSA.APR.B.2
6.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
List all possible rational zeros
f(x) = 3x5-5x2+x+6
Tags
CCSS.HSA.APR.B.2
CCSS.HSA.APR.B.3
7.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
How many roots or zeros does the equation
f(x) = 5x4-8x3+4x2-6x+3 have?
Tags
CCSS.HSA.APR.B.3
CCSS.HSA.REI.D.11
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