MATH 1148 Midterm: Exam 2 Review (AU 14)

A. Given the following function: f(x) = 4x10-44x9 + 201x8-504x7 + 756x6-684z? + 243x4 Factored form: f(x)x(2x -3)2(x-1)(x-3)3 . Determine the end behavior Find all zeros and their multiplicities Find all zeros of the polynomial function P(x) = x4 + χ3-13x2-7x + 42 algebraically, given that 2 and - 3 are some of the zeros of the function. Give exact values.

Consider the polynomial function p (x) = 5(x - 3)^2 (x - 2)^3 a.) List each real zero and its multiplicity. Zero:_________: Multiplicity: _______ Zero: _________: Multiplicity: ________ b) Determine whether the graph crosses, or touches the x-axis at each x-intercept. At x = ________, the graph crosses/touches the x-axis. (circle one) At x = _________, the graph crosses/touches the x-axis. (circle one) c) Determine the degree and the maximum number of turning points on the graph of p(x). d.) Describe the end-behavior of p(x). Form a polynomial function whose real zeros and degree are given. Zeros: -1, 1, 3; degree 3 Consider the rational function given by R(x) = x/x-4. a.) Find the domain of the function. b.) Find the vertical asymptote(s).

THEOREM A division. Write the polynomial in the form plx) - (2x3-x+1)-(x2+x+1) (4x22)+(-1) EXERCISES Bercises 1 -&. use poljnomial long division to perform the in Jer, + 3x-1)-(x-3) Sr-r+2r-1) (2+4) ses 7-20 use synthetic division to perform the indicated division. Write the polynomial in the form plx) 8. (x2-5)-(x-5) 10. (4x2-5x+3)+(x+3) 12, (4x3 + 2x-3)÷(x-3) 14. (42-1+ (x-1) 16, (3x3-x+4)÷(x-j) 18. (4x-12+132-12x+9)(x-) 20. (r6-6x+12x2-8)+(v2) 4-2x)+(x+) Im. (+8+x+2) ls Eaerciss 21 - 30, determine pic) using the Remainder Theorem p d «Q factor p(x)=(x-c)q(x). for the given polynomial functions and value of c. I 21.hx):2r2 _ x + 1, c 4 x) = 4x2-33x-18o, c=12 Dp(x)=x3 +2x2 + 3x + 4, ce-l 28, p(x) s 6x4-2 + 2, c=-1 29. eal zeros and factor the polynomial. 40, you are glven a polynomial and one ofits zeros, Use the techniques in this section to find the rest af the jd-24x2 +192x-512.に8 r'+2x2-3x-6, c=-2 ½ セタ2x3 .. x2-10x +5, e 4x4-28x3 +61x2-42x + 9, c is a zero of multiplicity 2 3x4-12-38x . 125x-275x 37x-12, c -1 is a zero of multiplicity 3 -2265r3-3213r2-1728x-324,c=-| is a zero of multiplicity -2x-2, c 1-v3 the leave om ces 41-45, create a polynomial the desi nial p which has the desired characteristics. You may