Question

#3, #4

3. (10 points) Solve the inequality analytically using a sign diagram and then give your answer in interval notation. (Make sure your sign diagram clearly identifies each zero (if any exist) as well as any values excluded from the domain. Use "+" or "-" to indicate whether the graph of the function that corresponds to the sign diagram is above or below the x-axis.) 2x - 2 54 X + 8 4. (10 points) Find all of the zeros of f(x) = 2x+ + x3 + 19x2 - 69x – 153 and then show the complete factorization over the complex numbers. Put the complex zeros in a + bi form. Zeros: Complete factorization of fover the complex numbers: f(x) =

Answer 1

given that 22 8 2기 2 8 4 드 | 오리- 2 -448) t8 오리2 -42 32 드 O 2+8 一22-34 드 0 +8 외7) 스 8 mo 가넷 t8 2 0 Lel- Ctrl) - X +17 t8 sts sign charlis > tve ve tve -17 18

hence f(21) is tve When e 378 and U s-17 f(a) ix ave, -ve, when ne(-17,-8) its solution ix . ale (-20, -17] V[ - 8,00) given that he f(21) = 2*+*+ 190?–692 - 153 = (2-3) (2x+3)(x²+24+7) hence To find its Zesos, e-3 22+3 FOS a e trut17 to when, When a-3 =0 d=3 2 at 3=0 x = -3 &

When , ar tra417 =0 2 =-1+ 41, -1-qi are henu, Zeos of f(2013 Zesos: -3, -3, (-1-4 i), (+1+4) over Complete factorizatim obf the complex Numberbit f(as)- be -3)(2+3)(1+1+-41) (2+1–41)