if (x-1) is the factor of the polynomial ( x3-2x2+mx-4 then find the value of m
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if (x-1) is the factor of the polynomial ( x3-2x2+mx-4 then find the value of m
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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