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 3 +10 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 3 +36 𝑥 2 =0 y = 2(x – 1)2 – 4 y = -(x + 2)3 𝑦=− 𝑥+3 +2 𝑦= 1 2 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 3 +28 𝑥 2 +36𝑥+16

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