E. Use the Lower and Upper Bound theorem to determine whether the given value of c is an upper bound, lower bound, or neither. 1. P(x) = x3 + 2x + 7; 0 = 5 2. P(x) = 4x3 - 7x2 - 11x + 5; C = -2 3. P(x) = x4 - x3 + x - 3x - 6; 0 = 1 4. P(x) = 2x1 - 9x3 - 18x2 + 71x - 30; 0 = -4 5. P(x) = X4 + 6x3 + 10x2 + 6x + 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 (m3). 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? 5x3 + 12. Graph the polynomialC. Verify whether the given value of A find the other roots of the given polynomial. 3 1. P(x) = 3x3 - 9x2 + 2x - 6; X = 2 NOT 2. P(x) = x3 - 11x2 + 39x - 45; X = 3 5 3. P(x) = 6x4 - 5x3 - 13x2 + 17x - 5; X = = 4. P(x) = 8x4 + 54x3 + 65x2 - 27x - 10; X = = 4 5. P(x) = 2x5 + x" - 12x3 - 6x2 + 16x + 88; X= 1 2 D. Determine all the rational roots for each given polynomial. 1. P(x) = x3 - 5x2 + 2x + 5 2. P(x) = 2x3 + 7x2 + 15x + 25 3. P(x) = X4 - x3 - x2 + x + 57 4. P(x) = 3x4 + 7x3 + 3x2 - 4 5. P(x) = 4x4 + x3 + 7x2 + 6x - 2 80 Math for Innovative Minds 10