Question

Show that 2x+1 is a factor of polynomial 2x^3-11x^2-4x+1

Answer 1

f(x) = 2x³-11x²-4x+1
If f(x) is divided by (2x+1), then f(-1/2) is the remainder.
f(-1/2) = 2(-1/2)³-11(-1/2)²-4(-1/2)+1
= 2(-1/8)-11(1/4)-4(-1/2)+1
= -1/4-11/4+2+1
= 3 - 12/4
= 3-3
= 0
(2x+1) is a factor of f(x) as remainder is zero.

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Answer 2

Hey there !!!!

If 2x+1=0 is a factor of p(x)=2x³-11x²-4x+1

then p(-1/2) =0

So,

p(x)=2x³-11x²-4x+1

p(-1/2) =2*(-1/2)³-11(-1/2)²-4*(-1/2)+1

           = -2/8-11/4+2+1
           =  -1/4-11/4+3
           =-12/4+3
           =-3+3=0

Therefore 2x+1 is a factor of p(x)=2x³-11x²-4x+1.

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