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Question Number 193087 by Abdullahrussell last updated on 03/Jun/23

Answered by Frix last updated on 03/Jun/23

x^4 +2x^3 −4x−2 (x+(1/2))^4 −(3/2)(x+(1/2))^2 −3(x+(1/2))−(3/(16)) ((x+(1/2))^2 −a(x+(1/2))−b)((x+(1/2))^2 +a(x+(1/2))−c) Comparing constants ⇒ ((x+(1/2))^2 −(√3)(x+(1/2))+(3/4)−((√3)/2))((x+(1/2))^2 +(√3)(x+(1/2))+(3/4)+((√3)/2)) ⇔ (x^2 +(1−(√3))x+1−(√3))(x^2 +(1+(√3))x+1+(√3)) This is your (x^2 +px+q)(x^2 +rx+s) (x+((1−(√3)−((12))^(1/4) )/2))(x+((1−(√3)+((12))^(1/4) )/2))(x+((1+(√3))/2)+(((12))^(1/4) /2)i)(x+((1+(√3))/2)−(((12))^(1/4) /2)i) This is your (x+t)(x+u)(+v)(x+w)

x4+2x3−4x−2(x+12)4−32(x+12)2−3(x+12)−316((x+12)2−a(x+12)−b)((x+12)2+a(x+12)−c)Comparingconstants⇒((x+12)2−3(x+12)+34−32)((x+12)2+3(x+12)+34+32)⇔(x2+(1−3)x+1−3)(x2+(1+3)x+1+3)Thisisyour(x2+px+q)(x2+rx+s)(x+1−3−1242)(x+1−3+1242)(x+1+32+1242i)(x+1+32−1242i)Thisisyour(x+t)(x+u)(+v)(x+w)

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