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Complete the sentence below. If 7 + 5i is a zero of a polynomial function of degree 5 with real coefficients, then so is If 7 + 5i is a zero of a polynomial function of degree 5 with real coefficients, then so isForm a polynomial f(x) with real coefficients having the given degree and zeros. Degree 4; zeros: 5 + 2i; 4 multiplicity 2 Let a represent the leading coefficient. The polynomial is f(x) = a(]) (Type an expression using x as the variable. Use integers or fractions for any numbers in the expression. Simplify your answer.)4x + 4 Solve the inequality R(x) $0, where R(x) = by using the graph of the function. The solution set for R(x) $ 0 is 2x + 4 (Type your answer in interval notation.) 6- y =2 + - -6 -4 2 X = - 2Use the graph shown to find the following. O (a) The domain and range of the function 8- (b) The intercepts, if any (c) Horizontal asymptotes, if any (d) Vertical asymptotes, if any (e) Oblique asymptotes, if any -1431 (a) What is the domain? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The domain of the function is {x /} (Type an inequality in the form x # . Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) O B. The domain of the function is the set of all real numbers. What is the range? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The range of the function is {y |}Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. Degree 4; zeros: i, 13 + i The remaining zero(s) of f is(are) (Use a comma to separate answers as needed.)Use the given zero to find the remaining zeros of the function. f(x) =x - 2x + 25x -50; zero: - 5i The remaining zero(s) of f is(are) (Use a comma to separate answers as needed.)Find the real solutions of the following equation. 11x + 15x - 25x + 7=0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The solution set is { } (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed. Type each answer only once.) O B. The solution set is @.Find the domain of the following rational function. 15x + x H(x) = 2 + 5 . . . Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The domain of H(x) is {x | }. (Type an inequality in the form x # . Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) O B. The domain of H(x) is the set of all real numbers.Use the graph of the function fto solve the inequality. a [a] x} > [J [b] fx) s O [a] The solution set for x) > 0 is E. [Type your answer in interval notation.) [b] The solution set for x) S l] is D. (Type your answer in interval notation.) Find the real zeros of f. Use the real zeros to factor f. f(x) = 29x + 30x +30x +1 The real zero(s) of f is/are (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) Factor f. f(x) =] (Factor completely. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.)Use the remainder theorem to find the remainder when f(x) is divided by x + 4. Then use the factor theorem to determine whether x + 4 is a factor of f(x). f(x) = 4x -64x + x -19 The remainder is Is x + 4 a factor of f(x) = 4x - 64x" + x 3 - 19? O No O YesOne solution of the equation x" - 19x+ 49x- 3=0 is 3. Find the sum of the remaining solutions. The sum of the remaining solutions is (Simplify your answer.)Use a transformation of the graph of y = x" to graph the function. f(x ) = (x- 2)3 +6 Select the graph of f(x) = (x - 2) +6. O A. O B. OC. OD. Ay Ay Ay AForm a polynomial whose zeros and degree are given. Zeros: - 6, multiplicity 1; -3, multiplicity 2; degree 3 Type a polynomial with integer coefficients and a leading coefficient of 1 in the box below. f(x) = (Simplify your answer.)Use the rational zeros theorem to list the potential rational zeros of the polynomial function. Do not attempt to find the zeros. f(x) = x - 11x + 10x - 13 Find the potential rational zeros. Choose the correct answer below. O A. - 1,1, - 13,13 1 1 O B. - 1,1, - 13, 13, - 13 13 1 1 O C. - 13,13, - 13' 13 1 1 OD. - 1,1, - 13 13Construct a polynomial function that might have the given graph. -2- Which of the following is a polynomial function that might have the given graph? 1 O A. f(x) = 7(x+1)(x - 1)(x-2)2 O B. f(x) = =(x+1)2(x-1)(x-2)2 1 O C. f(x) = - 5 (x+1)(x - 1)-(x-2) 1 O D. f(x) = 5(x+1)(x - 1)(x-2) 1 1 O E. f(x) = - 7(x+1)(x-1)(x - 2) OF. f(x) = =(x+1)(x- 1)2(x-2)Use a transformation of the graph of y = x" to graph the function. f (x ) = (x - 2)3 +6 Select the graph of f(x) = (x - 2) +6. O A. O B. O C. OD. Ay AY Ay Ay 12 12- A