3.6 Homework 1. The polynomial function P is given by P(x) = 3x(x + 1) (x - a), where a is a real number. Which of the following could be the graph of y = P(x) ? 2. Q(x) -4 389 -3 139 -2 35 -1 5 0 1 -1 2 -1 3 25 4 125 The table gives values of a polynomial function @ for selected values of . What is the degree of Q ? (A) 2 (B) 3 (C) 4 (D) 53. -NW 6 -5 - 4 O 2 3 5 -2- -3- -4+ Graph of P The graph of the polynomial function y - P(x) is shown. Which of the following could define P(a) ? (A) P(a) = (2-4)(1+3) 12 (B) P(x) = (2-4) (2+3) 12 (C) P(x) - (2+4)(1-3)2 12 (D) P(x) = (2+4)(x-3) 12 4. The function Q is a polynomial of degree 3. If @(5) = 0, which of the following must be true? (A) Q(-5) =0 (B) Q has two complex zeros. (C) Q(x) can be expressed as (x - 5) . P(x), where P(x) is a polynomial of degree 2. (D) Q(x) can be expressed as 7 , where P(x) is a polynomial of degree 4. 5. The leading term of the polynomial function p is an x", where a, is a real number and n is a positive integer. The factors of p include (x - 3), (x - i), and (2 - (2 + 2) ). What is the least possible value of n ? (A) 3 (B) 4 (C) (D) 66. A polynomial function has the form p(x) = ax' + bak, where a and b are nonzero constants, j and k are nonnegative integers. Which of the following conditions guarantees that p is an even function? 7. X O Graph of g The figure shown is the graph of a polynomial function g. Which of the following could be an expression for g(a) ? (A) 0.25(x - 5)(x - 1)(* + 8) (B) 0.25(x + 5) (x + 1)(x -8) (C) 0.25(x - 5) (x - 1)(1 + 8) (D) 0.25(x + 5) (x + 1)(x -8)