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.) 2.) Section 2 - Divide using Synthetic Division. 1.) 2.) 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 + 2 2.) (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.) 2.) 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)

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 3 +36 𝑥 2 =0

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: ____________________________________________________________

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.) 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: _______________________

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 3 +28 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: _______________________