Name ____________________________________________
Date_______________
Functions Overview
Synthetic Division
Independent Practice
1. María Eugenia used synthetic division to solve a Try It! Problem from his Algebra 2
Math Nation workbook. Her work is shown below.
María had the wrong solution for #3. Identify and correct her error.
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Section 1 Topic 4
2. Use synthetic division to write an equivalent expression for the rational expression
below.
12𝑚& − 11𝑚( + 9𝑚 + 18
3
𝑚+
4
3. Use synthetic division to write an equivalent expression for the rational expression
below.
2𝑡 & + 7𝑡 ( − 4𝑡 + 7
1
𝑡−
2
4. Use synthetic division to write an equivalent expression for the rational expression
below.
4𝑦 & + 3𝑦 ( − 9𝑦 + 2
1
𝑦−
4
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Section 1 Topic 4
5. Which of the following functions would satisfy 𝑑(𝑥) such that synthetic division can
be performed? Select all that apply.
5𝑥 5 + 3𝑥 & − 14𝑥 ( − 37𝑥 − 9
𝑑 𝑥
o 𝑥 −
o o o o o o 1
5
𝑥( − 5
−8 + 𝑥
2(𝑥 − 1)
5𝑥 67 + 1
𝑥 5−𝑥
4𝑥 − 7 + 𝑥
6. The polynomial 2𝑥 & − 13𝑥 ( + 17𝑥 − 10 represents the volume in cubic feet of a
rectangular water holding tank at Marlon’s Farm. The depth of the tank is
represented by the expression (𝑥 − 5) feet. The length is 17 feet. Let 𝑥 represent the
width of the tank.
Part A: Write an equivalent expression for the polynomial using the dimensions of
the tank.
Part B: Find the width of the tank. (Hint: It’s helpful to use synthetic division!)
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Section 1 Topic 4