1. Which of the following is a polynomial in one variable? a. 2y^2 + 2xy - 4x b. 3z^4 - 48z + 1 c. 5x^2 +5xy^2 -3 d. 8a^3b - 4^ab^2 2. Find the leading coefficient of f(x)= 3x^6 + 4x^2 + x -1 a. 2 b.3 c. 4 d. 6 3. which of the following is a complex number? a. x(5-6i) b. (x+5)(x-6) c. (x+y)(5x-y) d. 6y(x+y)(5x-y)(9x+2) 4. Write the polynomial of least degree with roots -2, 5, and 7 a. x^3 - 10x^2 + 11x + 70 b. x^3 +10x^2 + 11x - 70 c. x^3 - 14x^2 +59x - 70 d. x^3 + 14x^3 + 59x + 70 5. What is the nature of the roots of f(x)= x^2 + 4x + 16 a. two distinct real roots or zero b. one real double roots or zero c. no real roots or zeros d. more than two distinct real roots 6. Using Desartes' rule of signs, how many real roots does f(x)= 2x^3 +5x^2-x-3 contain? a. no positive real roots, no negative real roots b. two or zero positive real roots, one or zero negative real roots c. one or zero positive real roots, two or zero negative real roots d. two or zero positive real roots, two or zero negative real roots 7. Which of the following is a lower bound of f(x)= 3x^3 -2x^2 + x +2? a. -1 b.0 c. 1 d. 2 8. solve -1/x+5 lessthan or equal 2 (please show work) 9. Decompose x+3/ x^2-4 (please show work)