1. Algebra 2/Trigonometry Name: __________________________
Unit 4 Review Date: _______________ Block: ______
Directions: Complete all work on a separate piece of paper.
Section 1 - Divide using Long Division.
Section 2 - Divide using Synthetic Division.
1.) 2.)
1.) 2.)
Section 3 - Use the Remainder Theorem to evaluate each function at the given value.
Section 4 - Show that the given binomial is a factor of 𝑓(𝑥). Then find the remaining factors & zeros.
1.) f(-2) given
2.) g(3) given
𝑓 𝑥 =3 𝑥 3 +8 𝑥 2 +5𝑥−7
1.) 2.)
𝑓 𝑥 = 𝑥 3 −5 𝑥 2 −8𝑥+12;given (𝑥+2)
𝑔 𝑥 =4 𝑥 𝑥 2 −3𝑥−8
𝑓 𝑥 = 2 𝑥 4 +7𝑥 3 −4 𝑥 2 −27𝑥−18;
given (𝑥−2)(𝑥+3)
Section 5 - Identify the end behavior of each function, without referencing a graphing calculator.
Section 6 - Given the following zeros, find all of the linear factors and the least degree polynomial function.
1.) 2.)
3.)
𝑓 𝑥 =5−2𝑥−3 𝑥 2
1.) x = {4, -3, 1}
2.) x = {2, -5, 4i, -4i}
3.) x = {-3, 6, 3 , − 3 }
𝑓 𝑥 =2 𝑥 5 −5𝑥+7
𝑓 𝑥 =− 𝑥 3 +2 𝑥 2 +3𝑥−4
Section 7 - For each function, graph the parent graph (colored pencil) and the transformed graph (pencil).
Section 8 - Graph each piecewise function. Then, evaluate each when x = 2.
Section 9 – Solve each equation by factoring. Find all solutions.
1.) 𝑥 3 +2 𝑥 2 +2𝑥+4=0
2.) 𝑥 3 =−27
3.) 𝑥 4 + 𝑥 2 −20=0
4.) 𝑥 3 +4 𝑥 2 −𝑥=0
5.) 2 𝑥 4 −22 𝑥 𝑥 2 =0
y = 2(x – 1)2 – 4
y = -(x + 2)3
𝑦=− 𝑥+3 +2
𝑦= 𝑥 −1
I would also practice identifying the domain/range (in interval notation) of the graph, along with a description of it’s parent graph and transformations.
Section 10 - Write 𝑓(𝑥) as a product of linear factors and list all of its zeroes using the Rational Root Test. Then sketch a graph. Be sure to consider end behavior, plot the y-intercept, and calculate any turning points (minimum or maximum values). Use the graphs provided on the back.
1.)
𝑓 𝑥 = 𝑥 3 − 𝑥 2 −13𝑥−3
2.)
𝑓 𝑥 = 3𝑥 3 +2 𝑥 2 −19𝑥+6
3.)
𝑓 𝑥 = 𝑥 3 −4𝑥
4.)
𝑓 𝑥 = −𝑥 3 +7𝑥+6
5.)
𝑓 𝑥 =2 𝑥 3 +3 𝑥 2 −1
6.)
𝑓 𝑥 = 𝑥 4 +9𝑥 𝑥 2 +36𝑥+16

2. 4.) This graph has a turning point at (-1.53, -1.13). 5.)
Section 10 – Graphs. Be sure to consider end behavior, plot the y-intercept, and calculate any turning points (minimum or maximum values). Pay attention to the scale!
1.)
2.)
3.)
Use this scale:
x-axis  one block = ½
y-axis  one block = 2
Use this scale:
x-axis  one block = ½
y-axis  one block = 2
Use this scale:
x-axis  one block = ½
y-axis  one block = 1
4.) This graph has a turning point at (-1.53, -1.13).
5.)
6.) This graph has a turning point at (-1.31, -0.40).
Use this scale:
x-axis  one block = ½
y-axis  one block = 1
Use this scale:
x-axis  one block = ½
y-axis  one block = 1
Use this scale:
x-axis  one block = ½
y-axis  one block = 1