Math Analysis CP WS 4.X- Section Review A

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1 Math Analysis CP WS 4.X- Section Review Complete each question without the use of a graphing calculator.. Compare the meaning of the words: roots, zeros and factors.. Determine whether - is a root of x x x 0. Show your work.. Write a polynomial equation of least degree with roots, -, i, and -i. How many times does the graph of the related function intersect the x-axis? 4. What is the polynomial of least degree that has roots i, 0,?. Give an equation for a third degree polynomial that has roots at and a doule root at What do you know aout the roots of a quadratic equation if its discriminant is 0? 7. Solve x 6x 0y completing the square. 8. Find the discriminant of x 4x and descrie the nature of the roots of the equation. Then solve the equation using the quadratic formula How many times is - a root of x 8x 6 0? 0. Find the remainder of x 6x 9 x the inomial is a factor of the polynomial. and state whether. Find the remainder of x 4 6x 8 x the inomial is a factor of the polynomial.. Find the value of k so that the remainder of x x kx x is 0.. Find k such that x is a factor of and state whether 4 f( x) x x kx x. 4. One of the factors of x 7x 4x is x. What is another factor? 4. List all the possile rational roots of x x 6x 0. f x x x 6x. 6. Find all the zeros of 7. Find all the roots and factors of a 4 a Find all roots of the equation 4x x In the 6 x 8 rectangular garden, the paths (shaded), have equal widths. The garden s planting regions are shown as unshaded rectangles. If the total area of the shaded and unshaded regions is equal, how wide is each garden path? Math Analysis CP WS 4.X- Section Review A Do all work neatly and on a separate sheet of paper. List all of the possile rational roots of each equation. Then find all solutions (oth real and imaginary) of the equation.. x 4x x x x 0x x x 7x x 6 0 x x 4 0 Solve each equation m 8 0 m a 4 a a p p p p p Solve each inequality t t y y 0. x x Math Analysis CP WS 4.X- Section Review B. Solve each equation or inequality: a 6 6 a.. a a w w x 9 c. 0 x x d. x e. m f. a a 6. Use the graph of f(x) to solve f(x) < 0.. A Broadway theater sells 0 tickets for every performance. Each ticket costs $80. The company wants to increase the ticket price. They estimate that for each $ increase in ticket price, customers will e lost. Determine the ticket price that will allow the theater to increase its revenue y $ Consider the data elow: x y x.. 4 y a. Sketch a scatter plot of the data.. What type of equation would est model this? c. Find an equation f(x) to model the data. d. Find the approx values of x for which f(x) =

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3 Cumulative Algera Review- Chapter 04 Analysis CP All work is to e neatly shown on a separate piece of paper. Please write and ox your answer, including the multiple choice answer letter. This is due the school day after the chapter test.. What is the equation of a line with a y- intercept of and an x-intercept of -? (A) y 0.6x (B) y.7x (C) y x (D) y x (E) y x. If the second term in an arithmetic sequence is 4, and the tenth term is, what is the first term in the sequence? (A).8 (B).7 (C).8 (D).6 (E).7 f x x 6x, then what is the f x?. If minimum value of (A) -8.0 (B) -7.0 (C). (D) 6.0 (E).0 x x6 4. What value does approach as x x 6 approaches -? (A) -.67 (B) (C) 0 (D).00 (E).. If the greatest possile distance etween two points in a rectangular solid is, then which of the following could e the dimensions of this solid? (A) (B) 6 7 (C) 8 (D) 47 9 (E) Runner A travels a feet every minute. Runner B travels feet every second. In one hour, Runner A travels how much further than Runner B, in feet? (A) a 60 (B) a 60 (C) 60a 60 a (D) (E) 60a 60 x 7. If fx and gx 8. g f x (A) (B) x (C) x x (D) x (E) x x x! x! (A) 0. (B).0 (C) x (D) x x (E) x x, then x 9. In order to disprove the hypothesis "No numer divisile y is less than," it would e necessary to (A) prove the statement false for all numers divisile y (B) demonstrate that numers greater than are often divisile y (C) indicate that infinitely many numers greater than are divisile y (D) supply one case in which a numer divisile y is less than (E) show that a statement true of numers greater than is also true of numers less than x x4 0. The expression is undefined for x 0x8 what value(s) of x? x, 4 (A) (B) x (C) x 0 (D) x, 4 (E) x 0,, Written Response Question A complete response requires the following: Express your thinking in words Lael any figures you draw Identify any formulas used Make clear the source of numers used Full credit will not e earned if your work cannot clearly e followed. The final answer is important, ut meaningless if you cannot show someody how to get it Matt says that if a and are any positive numers, then a must e smaller than a. a. Choose three specific pairs of numers to test Matt's statement.. Suppose a a. Use algera to determine what this implies aout the value of a or. Hint: Start y squaring oth sides. c. Based on what you discovered in part, what can you determine aout Matt's initial assumption aout a and?

4 d. For any triangle, the sum of the smaller two sides must e greater than the length of the third side. Using the given triangle, determine if Matt's statement is true or false. a c

5 Math Analysis CP