Algebra 2/Trigonometry Unit 3 Review & Test Review
Review and test questions covering various algebraic and trigonometric topics such as division, synthetic division, remainder theorem, factorization, end behavior analysis, identifying zeros, solving equations by factoring, and graphing polynomials.
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Algebra 2/Trigonometry Unit 3 Review Directions: Complete all work on a separate piece of paper. Section 1 - Divide using Long Division. 1.) 3) (x 12) 10x (2x2 + + + Name: __________________________ Date: _______________ Block: ______ Section 2 - Divide using Synthetic Division. 15x 17x - (3x + 1.) - 25) (x - 5) 3 2 (x 5x 6x x - 2) (x 2) 4 3 2 + + + 2.) - (5x - 6x 8) (x - 4) 3 2 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 ?(?). Then find the remaining factors & zeros. 1.) f(-2) given ? ? = 3?3+ 8?2+ 5? 7 ? ? = ?3 5?2 8? + 12;given (? + 2) ? ? = 2?4+ 7?3 4?2 27? 18; 1.) 2.) 2.) g(3) given ? ? = 4?3+ 10?2 3? 8 given (? 2)(? + 3) Section 5 - Identify the end behavior of each function, without referencing a graphing calculator. ? ? = 5 2? 3?2 1.) 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} 2.) ? ? = 2?5 5? + 7 ? ? = ?3+ 2?2+ 3? 4 3.) 3.) x = {-3, 6, 3, 3} Algebra 2/Trigonometry Unit 3 Review Directions: Complete all work on a separate piece of paper. Section 1 - Divide using Long Division. 1.) 3) (x 12) 10x (2x2 + + + Name: __________________________ Date: _______________ Block: ______ Section 2 - Divide using Synthetic Division. 15x 17x - (3x + 1.) - 25) (x - 5) 3 2 (x 5x 6x x - 2) (x 2) 4 3 2 + + + 2.) - (5x - 6x 8) (x - 4) 3 2 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 ?(?). Then find the remaining factors & zeros. 1.) f(-2) given ? ? = 3?3+ 8?2+ 5? 7 ? ? = ?3 5?2 8? + 12;given (? + 2) ? ? = 2?4+ 7?3 4?2 27? 18; 1.) 2.) 2.) g(3) given ? ? = 4?3+ 10?2 3? 8 given (? 2)(? + 3) Section 5 - Identify the end behavior of each function, without referencing a graphing calculator. ? ? = 5 2? 3?2 1.) 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} 2.) ? ? = 2?5 5? + 7 ? ? = ?3+ 2?2+ 3? 4 3.) 3.) x = {-3, 6, 3, 3}
Section 7 Solve each equation by factoring. Find all solutions. 1.) ?3+ 2?2+ 2? + 4 = 0 2.) ?3= 27 3.) ?4+ ?2 20 = 0 4.) ?3+ 4?2 ? = 0 5.) 2?4 22?3+ 36?2= 0 Section 8 - Write ?(?) 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! ? ? = ?3 ?2 13? 3 1.) 2.) ? ? = ?3+ ?2+ 4? + 4 4.) 3.) ? ? = ?3 4? ? ? = ?3+ 7? + 6 *6.) 5.) ? ? = ?3 3?2+ 4? 2 ? ? = 2?3+ 3?2 1 *8.) *7.) ? ? = 3?3+ 2?2 19? + 6 ? ? = ?4+ 9?3+ 28?2+ 36? + 16 Section 7 Solve each equation by factoring. Find all solutions. 1.) ?3+ 2?2+ 2? + 4 = 0 2.) ?3= 27 3.) ?4+ ?2 20 = 0 4.) ?3+ 4?2 ? = 0 5.) 2?4 22?3+ 36?2= 0 Section 8 - Write ?(?) 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! ? ? = ?3 ?2 13? 3 1.) 2.) ? ? = ?3+ ?2+ 4? + 4 4.) 3.) ? ? = ?3 4? ? ? = ?3+ 7? + 6 *6.) 5.) ? ? = ?3 3?2+ 4? 2 ? ? = 2?3+ 3?2 1 *8.) *7.) ? ? = 3?3+ 2?2 19? + 6 ? ? = ?4+ 9?3+ 28?2+ 36? + 16
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: ____________________________________________________________ Relative Min/Max: (0,-1) 6.) 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: ____________________________________________________________ * Hint: Don t forget how a double root impacts the graph! 8.) 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: ____________________________________________________________
