SOLUTION: Fully factor the third-order polynomial H(s) if it is known that one of the factors is (s+2). H(s)= 2s^3-7s^2-43s-42 I need help....

Question 22646: Fully factor the third-order polynomial H(s) if it is known that one of the factors is (s+2).
H(s)= 2s^3-7s^2-43s-42
I need help....
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
H(s)= 2s^3-7s^2-43s-42 try s=0,1,2,-1,-2 etc..
we find that at s=2 ....H=0...HENCE S+2 IS A FACTOR
DIVIDING WITH S+2 WE GET
-2...|...2......-7.........-43.........-42
.....|...0......-4..........22..........42
..............................................
.........2......-11.........-21..........0
HENCE WE GET 2S^2-11S-21
=2S^2-14S+3S-21=2S(S-7)+3(S-7)=(2S+3)(S-7)..HENCE
H(S)=(S+2)(2S+3)(S-7)

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