Algebra 2/Trigonometry
Name: __________________________
Unit 3 Review
Date: _______________ Block: ______
Directions: Complete all work on a separate piece of paper.
Section 1 - Divide using Long Division.
1.)
(2x2  10x  12)  (x  3)
3
2
1.) (3x - 17x  15x - 25)  (x - 5)
2.) (x 4  5x3  6x2 - x - 2)  (x  2)
Section 3 - Use the Remainder Theorem to
evaluate each function at the given value.
1.) f(-2) given
2.) g(3) given
𝑓 𝑥 = 3𝑥 3 + 8𝑥 2 + 5𝑥 − 7
3
Section 2 - Divide using Synthetic Division.
2
𝑔 𝑥 = 4𝑥 + 10𝑥 − 3𝑥 − 8
Section 5 - Identify the end behavior of each
function, without referencing a graphing
calculator.
2.) (5x3 - 6x2  8)  (x - 4)
Section 4 - Show that the given binomial is a
factor of 𝑓(𝑥). Then find the remaining factors
& zeros.
3
2
1.) 𝑓 𝑥 = 𝑥 − 5𝑥 − 8𝑥 + 12; given (𝑥 + 2)
2.) 𝑓 𝑥 = 2𝑥 4 + 7𝑥 3 − 4𝑥 2 − 27𝑥 − 18;
given (𝑥 − 2)(𝑥 + 3)
Section 6 - Given the following zeros, find all of
the factors and the least degree polynomial
function.
𝑓 𝑥 = 5 − 2𝑥 − 3𝑥 2
1.)
x = {4, -3, 1}
2.) 𝑓 𝑥 = 2𝑥 5 − 5𝑥 + 7
2.)
x = {2, -5, 4i, -4i}
3
2
3.) 𝑓 𝑥 = −𝑥 + 2𝑥 + 3𝑥 − 4
3.)
x = {-3, 6, 3, − 3}
1.)
Algebra 2/Trigonometry
Name: __________________________
Unit 3 Review
Date: _______________ Block: ______
Directions: Complete all work on a separate piece of paper.
Section 1 - Divide using Long Division.
1.)
(2x2  10x  12)  (x  3)
3
2
1.) (3x - 17x  15x - 25)  (x - 5)
4
3
2
2.) (x  5x  6x - x - 2)  (x  2)
Section 3 - Use the Remainder Theorem to
evaluate each function at the given value.
1.) f(-2) given
2.) g(3) given
𝑓 𝑥 = 3𝑥 3 + 8𝑥 2 + 5𝑥 − 7
3
Section 2 - Divide using Synthetic Division.
2
𝑔 𝑥 = 4𝑥 + 10𝑥 − 3𝑥 − 8
Section 5 - Identify the end behavior of each
function, without referencing a graphing
calculator.
2.) (5x3 - 6x2  8)  (x - 4)
Section 4 - Show that the given binomial is a
factor of 𝑓(𝑥). Then find the remaining factors
& zeros.
3
2
1.) 𝑓 𝑥 = 𝑥 − 5𝑥 − 8𝑥 + 12; given (𝑥 + 2)
2.) 𝑓 𝑥 = 2𝑥 4 + 7𝑥 3 − 4𝑥 2 − 27𝑥 − 18;
given (𝑥 − 2)(𝑥 + 3)
Section 6 - Given the following zeros, find all of
the factors and the least degree polynomial
function.
𝑓 𝑥 = 5 − 2𝑥 − 3𝑥 2
1.)
x = {4, -3, 1}
2.) 𝑓 𝑥 = 2𝑥 5 − 5𝑥 + 7
2.)
x = {2, -5, 4i, -4i}
3
2
3.) 𝑓 𝑥 = −𝑥 + 2𝑥 + 3𝑥 − 4
3.)
x = {-3, 6, 3, − 3}
1.)
Section 7 – Solve each equation
by factoring. Find all solutions.
1.) 𝑥 3 + 2𝑥 2 + 2𝑥 + 4 = 0
2.) 𝑥 3 = −27
3.) 𝑥 4 + 𝑥 2 − 20 = 0
4.) 𝑥 3 + 4𝑥 2 − 𝑥 = 0
5.) 2𝑥 4 − 22𝑥 3 + 36𝑥 2 = 0
Section 8 - Write 𝑓(𝑥) as a product of factors and list all of its zeros. You must verify all rational zeros!
Use your calculator to find the relative maxima/minima (to the nearest hundredths). Then sketch a
graph. * You should be able to do problems 6-8 without a graphing calculator!
1.)
𝑓 𝑥 = 𝑥 3 − 𝑥 2 − 13𝑥 − 3
𝑓 𝑥 = 𝑥 3 + 𝑥 2 + 4𝑥 + 4
4.)
𝑓 𝑥 = −𝑥 3 + 7𝑥 + 6
𝑓 𝑥 = 𝑥 3 − 3𝑥 2 + 4𝑥 − 2
*6.)
𝑓 𝑥 = 2𝑥 3 + 3𝑥 2 − 1
𝑓 𝑥 = 3𝑥 3 + 2𝑥 2 − 19𝑥 + 6
*8.)
𝑓 𝑥 = 𝑥 4 + 9𝑥 3 + 28𝑥 2 + 36𝑥 + 16
3.)
𝑓 𝑥 = 𝑥 3 − 4𝑥
5.)
*7.)
2.)
Section 7 – Solve each equation
by factoring. Find all solutions.
1.) 𝑥 3 + 2𝑥 2 + 2𝑥 + 4 = 0
2.) 𝑥 3 = −27
3.) 𝑥 4 + 𝑥 2 − 20 = 0
4.) 𝑥 3 + 4𝑥 2 − 𝑥 = 0
5.) 2𝑥 4 − 22𝑥 3 + 36𝑥 2 = 0
Section 8 - Write 𝑓(𝑥) as a product of factors and list all of its zeros. You must verify all rational zeros!
Use your calculator to find the relative maxima/minima (to the nearest hundredths). Then sketch a
graph. * You should be able to do problems 6-8 without a graphing calculator!
1.)
𝑓 𝑥 = 𝑥 3 − 𝑥 2 − 13𝑥 − 3
𝑓 𝑥 = 𝑥 3 + 𝑥 2 + 4𝑥 + 4
4.)
𝑓 𝑥 = −𝑥 3 + 7𝑥 + 6
𝑓 𝑥 = 𝑥 3 − 3𝑥 2 + 4𝑥 − 2
*6.)
𝑓 𝑥 = 2𝑥 3 + 3𝑥 2 − 1
𝑓 𝑥 = 3𝑥 3 + 2𝑥 2 − 19𝑥 + 6
*8.)
𝑓 𝑥 = 𝑥 4 + 9𝑥 3 + 28𝑥 2 + 36𝑥 + 16
3.)
𝑓 𝑥 = 𝑥 3 − 4𝑥
5.)
*7.)
2.)
Algebra 2/Trigonometry
Test Review Graphing
Name: __________________________
Date: ________________ Block: _____
Section 8– Write f(x) as a product of linear factors and list all of its zeros. You must verify all rational zeros
(using synthetic division). Use our calculator to find the relative maxima and minima (to the nearest hundreth).
Then sketch a graph.
1.)
End Behavior: As x, f(x) ______, As x-, f(x) ______
y-intercept: ________
Product of Linear Factors: _____________________________ Zeros: _______________________
Relative Minima/Maxima: ____________________________________________________________
2.)
End Behavior: As x, f(x) ______, As x-, f(x) ______
y-intercept: ________
Product of Linear Factors: _____________________________ Zeros: _______________________
Relative Minima/Maxima: ____________________________________________________________
Algebra 2/Trigonometry
Test Review Graphing
Name: __________________________
Date: ________________ Block: _____
Section 8 – Write f(x) as a product of linear factors and list all of its zeros. You must verify all rational zeros
(using synthetic division). Use our calculator to find the relative maxima and minima (to the nearest hundreth).
Then sketch a graph.
3.)
End Behavior: As x, f(x) ______, As x-, f(x) ______
y-intercept: ________
Product of Factors: _____________________________ Zeros: _______________________
Relative Minima/Maxima: ____________________________________________________________
4.)
End Behavior: As x, f(x) ______, As x-, f(x) ______
y-intercept: ________
Product of Factors: _____________________________ Zeros: _______________________
Relative Minima/Maxima: ____________________________________________________________
Algebra 2/Trigonometry
Test Review Graphing
Name: __________________________
Date: ________________ Block: _____
Section 8– Write f(x) as a product of linear factors and list all of its zeros. You must verify all rational zeros
(using synthetic division). Use our calculator to find the relative maxima and minima (to the nearest hundreth).
Then sketch a graph.
5.)
End Behavior: As x, f(x) ______, As x-, f(x) ______
y-intercept: ________
Product of Factors: _____________________________ Zeros: _______________________
Relative Minima/Maxima: ____________________________________________________________
6.)
Relative Min/Max:
(0,-1)
End Behavior: As x, f(x) ______, As x-, f(x) ______
y-intercept: ________
Product of Factors: _____________________________ Zeros: _______________________
Relative Minima/Maxima: ____________________________________________________________
Algebra 2/Trigonometry
Test Review Graphing
Name: __________________________
Date: ________________ Block: _____
Section 8– Write f(x) as a product of linear factors and list all of its zeros. You must verify all rational zeros
(using synthetic division). Then sketch a graph.
7.)
Relative Min/Max:
(-1.69,29.34)
(1.25, -8.77)
End Behavior: As x, f(x) ______, As x-, f(x) ______
y-intercept: ________
Product of Factors: _____________________________ Zeros: _______________________
Relative Minima/Maxima: ____________________________________________________________
8.)
* Hint: Don’t forget how a double root impacts the graph!
Relative Min/Max:
(-3.44, -2.83)
(-1.31,-0.40)
End Behavior: As x, f(x) ______, As x-, f(x) ______
y-intercept: ________
Product of Factors: _____________________________ Zeros: _______________________
Relative Minima/Maxima: ____________________________________________________________