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The-polynomial-P-x-x-3-ax-2-4x-b-where-a-and-b-are-constants-Given-that-x-2-is-a-factor-of-P-x-and-that-a-remainder-of-6-is-obtained-when-P-x-is-divided-by-x-1-find-the-values-of-a-and-b-




Question Number 107428 by abony1303 last updated on 10/Aug/20
The polynomial P(x)=x^3 +ax^2 −4x+b,  where a and b are constants. Given that  x−2 is a factor of P(x) and that a remainder  of 6 is obtained when P(x) is divided by  (x+1), find the values of a and b.
ThepolynomialP(x)=x3+ax24x+b,whereaandbareconstants.Giventhatx2isafactorofP(x)andthataremainderof6isobtainedwhenP(x)isdividedby(x+1),findthevaluesofaandb.
Commented by abony1303 last updated on 10/Aug/20
pls help
plshelp
Answered by mr W last updated on 10/Aug/20
P(x)=x^3 +ax^2 −4x+b  P(x)=(x−2)Q(x)  P(2)=0  2^3 +a×2^2 −4×2+b=0  ⇒4a+b=0   ...(i)    P(x)=(x+1)R(x)+6  P(−1)=6  (−1)^3 +a(−1)^2 −4(−1)+b=6  ⇒a+b=3   ...(ii)  ⇒a=−1  ⇒b=4
P(x)=x3+ax24x+bP(x)=(x2)Q(x)P(2)=023+a×224×2+b=04a+b=0(i)P(x)=(x+1)R(x)+6P(1)=6(1)3+a(1)24(1)+b=6a+b=3(ii)a=1b=4

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