Collge Algebra - Spring 2016 Exam 4 - (Ch. 6, parts of Ch. 7 & 8) Name__________________________________ 1) Given the graph of a polynomial function, f(x), answer the following questions. 19 pts a) Determine whether the degree of the polynomial function is even or odd. How do you know? b) What is the most likely degree of this polynomial function? c) Determine whether the leading coefficient is positive or negative. How do you know? d) Utilizing the information from parts a-c, write a polynomial function that could represent the graph above. (Leave the equation in factored form.) e) State the x-interval(s) for which f(x) < 0. f) Circle all that apply to this function: Contains a local maximum Contains an absolute maximum Contains a local mimimum Contains an absolute minimum The domain is all real numbers The range is all real numbers 1 Solve the polynomial equation. 3 pts 2) (x + 3)2(x - 6)(5x - 5) = 0 2) Solve the polynomial equation by factoring. 4 pts 3) 3x2 + 14x - 24 = 0 3) Use synthetic division to find the quotient and remainder. 4 pts 4) (5x3 - 8x2 - 15x + 2) (x - ) 4) Explain or show how to determine whether the second polynomial is a factor of the first polynomial. 5 pts 5) (4x3 + 10x2 + 11x + 14); (x + 2) One solution of a polynomial equation is given. Use synthetic division to find any remaining solutions. 5 pts 6) 2x3 + 7x2 - 17x - 10 = 0; x = -5 6) Solve the equation exactly in the complex number system. 5 pts 7) x3 - 9x 2 + 16x - 144 = 0 Solve. 5 pts -8 3 x = 8) 2x 6 3x 7) 8) 2 For #9-10, give the equations, if any exist, of A) vertical asymptote(s) and B) horizontal asymptote(s) of the rational functions. 4 pts each 8x + 5 9) f(x) = 9) -2x + 12 10) f(x) = 6x - 5 x2 + 1 10) Use algebraic and/or graphical methods to solve the inequality. 5 pts x + 22 <5 11) x+1 for problems 12-14, solve. 5 pts each 12) the profit function a product is given by p(x) =-0.6x3 + 54x2 135x - 12,150 dollars, where x number of units produced and sold. determine levels production sale that give greater than 0. 13) future value $6000 invested 6 years at rate r, compounded annually, s =6000(1 r)6 . find as percent, gives $9,800.00. round to nearest tenth percent. 14) in following formula, y minimum hours studying required attain 0.48x test score x: how many study are needed 88? 100.5 if necessary. 3 write augmented matrix associated with system solution system. 2x z =-3 15) y-z =7 5z =-20 graph region inequalities. 5x 3y 9 16)> 1 x 0 Graph the solution region for the system of inequalities. 5 pts 2 17) y x - 5 -4x + 5y > 10 Extra Credit!!! Solve the system. 4 pts 18) xy = 12 2x - y = 5 18) 4