using factor theorem prove that (x+2)(x-1) is a factor of polynomial x⁴+x³+2x²+4x-8
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x+2=0
=>x=-2
f(x)=x^4+x^3+2x^2+4x-8
Using remainder theorem
f(2)=-2^4+-2^3+2×-2^2+4×-2-8
=16-8-8-8-8
=16-16-8-8
=0
°•°f(x)=0
•°•(x+2) is a factor of f(x)
x-1=0
=>x=1
Using remainder theorem
f(1)=1^4+1^3+2×1^2+4×1-8
=1+1+2+4-8
=8-8
=0
°•°f(x)=0
•°•(x-1) is a factor of f(x)
=>x=-2
f(x)=x^4+x^3+2x^2+4x-8
Using remainder theorem
f(2)=-2^4+-2^3+2×-2^2+4×-2-8
=16-8-8-8-8
=16-16-8-8
=0
°•°f(x)=0
•°•(x+2) is a factor of f(x)
x-1=0
=>x=1
Using remainder theorem
f(1)=1^4+1^3+2×1^2+4×1-8
=1+1+2+4-8
=8-8
=0
°•°f(x)=0
•°•(x-1) is a factor of f(x)
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