Question

By using remainder theorm,show that 2x-1 is a factor of the polynomial f(x)=4x^3+8x^2-x-2​

Answer 1

Remainder theorem

q(x) is a factor of polynomial p(x) then p(x) = 0

Since q(x) = 2x-1 is a factor of f(x)

then f(x) =0

Let 2x - 1 =0

2x -1 +1= 0+1 ...........adding both side by 1

2x = 1

2x/2 =1/2....….. Dividing both side by 2

x = 1/2

Now put x= 1/2 in f(x)

f(x) = 4(1/2)^3 + 8(1/2)^2 - (1/2) - 2

>>>>> 4*(1)^3/2^3 + 8*(1)^2/2^2-5/2

>>>>> 4*1/8 + 8*1/4 -5/2

>>>>> 1/2 + 2 - 5/2 = 5/2 -5/2 =0

Hence f(x) =0

therefore 2x-1 is factor of f(x)

ANS.