for additional discussion and activities on this topic. Math Empowerment A. Identify which of the following is a polynomial equation. 1. P(x) = -4x3 + 2x2 + 5 . Vx - 4 = 0Vx - 4 =0 2. x = 1i, 2 1 2x = ti, 2 + VZ 5. (2x - 5) (x + 2) = 0 3. x - 16 = 0 B. Identify the number of rational, irrational, and imaginary roots for each polynomial by completing the table. Number of Number of Number of Polynomial Equation Rational Roots Irrational Roots Imaginary Roots x2 + 2x + 5 =0 0 3x2- 11x - 20 = 0 0 2x3- x - 16x + 8=0 x' - x+ 2x2 - 4x - 8 =0 2 x + x - 2x3 - 2x2 - 3x - 3 =02. P(x) = 4x3 - 7x2 - 11x + 5; 0 = -2 3. P(X) = X1 - x3 + x2 - 3x - 6;0 = 1 4. P(x) = 2x4 -9x3- 18x3 + 71x - 30; 0 = 4 5. P(x) = x* + 6x3 + 10x3 + 6x 4 9: 0 = 6 F. Read and answer each problem. 1. Find a polynomial that has rational roots, 1, -2, and 4 with P(1) = 3. 2. Suppose 3x - 1, 4x - 2, and 3x + 1 are three consecutive integers. Find these integers such that their product is 210. 3. A shipping container in the shape of a rectangle must have a volume of 84 cubic meters (m ). If the length of the container is 1 meter longer than the width, and the height is 1 meter than twice the width, what are the dimensions of the container? 4. List all the possible rational roots of P(x) = 2x* + 5x + 12. Graph the polynomial using an online graphing tool and explain why it has no rational roots. 5. Show that v2 is irrational using the Rational Root theorem