List all possible rational zeros given by the Rational Zeros Theorem. Do not check to see which actually are zeros. P(x)= 2x+8x3+ 3x2 - 26 1 13 O a. * = +26, x = +1, x = ±2, x = + 7.x= +13, x = ± O b. X = +1, x = +2, x = + x= ±13 37 1 Oc.x= +26, x = +1, x = ±2,x = 37 13 Od.x= +26, x = ±1, x = +3, x = ± x = ±13, x = ± O e. x = +26, x = ±1, x = +2, x + x = +13 38

3. For the function f(x) = 2x4 – 5x3 + 9x² + x – 15: a. State the degree of the polynomial b. State the number of zeros the polynomial function will have. c. Use the Rational Zero Theorem to find all of the possible rational zeros d. Look at the graph or Table on a graphing calculator to determine which numbers on the list of rational zeros are real zeros indicated by the x-intercepts of the graph. In the space below, use synthetic division to verify one rational zero. Note: If the division remainder is zero, the number divided is a zero of the function. е. f. Find all remaining zeros. (Show work!) Note: Use the reduced polynomial (the quotient from the division) to continue the search for zeros © If the degree of the reduced polynomial is higher than 2, continue the synthetic division process with another real zero. (Remember: a number may be a multiple zero – i.e. occur more than once ) © Whenever the reduced polynomial is quadratic, the zeros can be found by using methods for…

§14.7 #10,14,16,32,34,36,42,50. II1. Suppose f(x, y) has continuous partial derivatives on R² and Vf(1,7) = 0, frr (1, 7) = –5, fyy(1, 7) = –3, and fry(1, 7) = –2. Indicate which of the following is definitely true (no reasons nec- essary): f has a local minimum at (1, • f has a local maximum at (1,7); • f has a saddle point at (1, 7). xx 7);

Is x + 5 rational or not? is 2/ x-5 rational or not?