Question

if (x-1) is the factor of the polynomial (x3-2x^2+mx-4) then find the value of m.

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Answer 1

Step-by-step explanation:

Since (x−1) and (x+3) are factors

By remainder theorem

x−1=0 and x+3=0

∴x=1 and x=−3

∴p(1) and (P(−3)) must be equal to zero.  

∴p(1)=13−m(1)2−13(1)+n

∴−12−m+n=0

∴n−m=12−−−−−(1)

Also p(−3)=(−3)3−9m+39+n=0

∴−27−9m+39+n=0

∴12=9m−n−−−−−(2)

∴ by (1) and (2)

10m=2m;n=5m

∴4m=12;m=3

∴n=3×5=15

∴m=3 and n=15