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.
1.) )
Section 2 - Divide using Synthetic Division.
1.) )
Section 3 – Showing all work, determine if each of the following is factor of the polynomial.
1.) (x-1) given f(x) = 2x4 + 3x3 – 4x2 – 3x ) (x-3) given g(x)= 4x3 + 10x2 – 3x – 8
Section 4 - Show that the given binomial is a factor of 𝑓(𝑥). Then find the remaining factors & zeros.
1.) )
𝑓 𝑥 = 𝑥 3 −5 𝑥 2 −8𝑥+12;given (𝑥+2)
𝑓 𝑥 = 2 𝑥 4 +7𝑥 3 −4 𝑥 2 −27𝑥−18;
given (𝑥−2)(𝑥+3)

2. 𝑓 𝑥 =5−2𝑥−3 𝑥 2 𝑓 𝑥 =2 𝑥 5 −5𝑥+7 𝑓 𝑥 =− 𝑥 3 +2 𝑥 2 +3𝑥−4
Section 5 - Identify the end behavior of each function, without referencing a graphing calculator.
1.)
2.)
3.)
𝑓 𝑥 =5−2𝑥−3 𝑥 2
𝑓 𝑥 =2 𝑥 5 −5𝑥+7
𝑓 𝑥 =− 𝑥 3 +2 𝑥 2 +3𝑥−4
Section 6 - Given the following zeros, find all of the factors and the least degree polynomial function.
1.) x = {4, -3, 1}
2.) x = {2, -5, 4i, -4i}
3.) x = {-3, 6, 3 , − 3 }
Section 7 – 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

3. 1.) 2.) Algebra 2/Trigonometry Name: __________________________
Test Review Graphing 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 hundredth). Then sketch a graph.
1.)
𝑓 𝑥 = 𝑥 3 − 𝑥 2 −13𝑥−3
End Behavior: As x-, f(x) ______, As x, f(x) ______ y-intercept: ________
Product of Factors: _____________________________ Zeros: _______________________
Relative Minima/Maxima: ____________________________________________________________
2.)
𝑓 𝑥 = 𝑥 3 + 𝑥 2 +4𝑥+4
End Behavior: As x-, f(x) ______, As x, f(x) ______ y-intercept: ________
Product of Factors: _____________________________ Zeros: _______________________
Relative Minima/Maxima: ____________________________________________________________

4. 3.) 4.) Algebra 2/Trigonometry Name: __________________________
Test Review Graphing 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 hundredth). Then sketch a graph.
3.)
𝑓 𝑥 = 𝑥 3 −4𝑥
End Behavior: As x-, f(x) ______, As x, f(x) ______ y-intercept: ________
Product of Factors: _____________________________ Zeros: _______________________
Relative Minima/Maxima: ____________________________________________________________
4.)
𝑓 𝑥 = −𝑥 3 +7𝑥+6
End Behavior: As x-, f(x) ______, As x, f(x) ______ y-intercept: ________
Product of Factors: _____________________________ Zeros: _______________________
Relative Minima/Maxima: ____________________________________________________________

5. 5.) 6.) Algebra 2/Trigonometry Name: __________________________
Test Review Graphing 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 hundredth). Then sketch a graph.
5.)
𝑓 𝑥 = 𝑥 3 −3 𝑥 2 +4𝑥−2
End Behavior: As x-, f(x) ______, As x, f(x) ______ y-intercept: ________
Product of Factors: _____________________________ Zeros: _______________________
Relative Minima/Maxima: ____________________________________________________________
** NON – CALC!!!! 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. (*Remember: Turning points do not need to be exact since you may not use a graphing calculator)
6.)
𝑓 𝑥 = 2𝑥 3 +3 𝑥 2 −1
Possible Roots: __________________________________________________________________
End Behavior: As x-, f(x) ______, As x, f(x) ______ y-intercept: ________
Product of Factors: _____________________________ Zeros: _______________________

6. 7.) 8.) Algebra 2/Trigonometry Name: __________________________
Test Review Graphing Date: ________________ Block: _____
** NON – CALC!!!! 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. (*Remember: Turning points do not need to be exact since you may not use a graphing calculator)
7.)
𝑓 𝑥 = 3𝑥 3 +2 𝑥 2 −19𝑥+6
Possible Roots: __________________________________________________________________
End Behavior: As x-, f(x) ______, As x, f(x) ______ y-intercept: ________
Product of Factors: _____________________________ Zeros: _______________________
8.)
𝑓 𝑥 = 𝑥 4 +9𝑥 𝑥 2 +36𝑥+16
* Hint: Don’t forget how a double root impacts the graph!
Possible Roots: __________________________________________________________________
End Behavior: As x-, f(x) ______, As x, f(x) ______ y-intercept: ________
Product of Factors: _____________________________ Zeros: _______________________