The answers are in the 3rd picture

Can you also explain how you get the multiplicities, I really don't understand that part

Page 1 of 5 For each function: a) List all possible rational zeros. b) Use Descartes Rule of signs to find how many possible positive real zeros, how many negative real zeros, and how many imaginary zeros there are. c) Use synthetic division to find the zeros. d) Use the zeros to factor the polynomial function and sketch a rough graph. 1. f(x) = x3 - 2x2 - 5x+6 2. f(x) = x4 -9x2 -4x+12 3. f(x) = 13 -7x2+x-7 4. f(x)=3x3 +3x2 -11x-105. f (x) = 9x -5x- -x 6. f(x) =x4+2x2 -15 7. S(x) =x5 - 2x4 -4x+8 8. f(x)=x5 -60x3 -80x2 +960x+ 2304Page 5 of Answers 1-8 part c. and d. only. For graphs check desmos.com or your graphing calculator. 1. x=-2, x=1, x=3 (each has mult. 1), f(x) = (x+2)(x-1)(x-3) 2. x=-2 (mult. 2), x=1 (mult. 1), x=3 (mult. 1) f(x) = (x+2)2 (x-1)(x-3) 3. x=7 (mult. 1) , f(x) = (x-7)(x2+1) 4. x=-2, x= 3+ 169 (each has mult. 1) f(x) = (x+2)(x_ 3+V69. -) (x - 3-V69 6 6 5. x=0, x: 5+161 (each has mult. 1) f(x) = (x)(x- 5+v61 )(x_ 5-161 18 18 18 6. x=13 (each has mult. 1) f(x) = (x - V3) (x + V3) (x2+5) 7. 'x=2, x=+2 (each has mult. 1) f(x) = (x - V2) (x + v2) (x - 2)(x2+2) 8. x=-4 (mult. 3), x=6 (mult. 2) f(x) = (x+4)3(x-6)2 V29 9. Zeros: x =- 3 3 13 10. Zeros: x=-5, x= 2 2