Question

find the remainder and tell weather 2x-1 is a factor of 2xcube -xsquare +3x-1 or not

Answer 1

Given p(x) = 2x^3 - x^2 + 3x - 1.

Given g(x) = 2x - 1.

Apply remainder theorem, we get

= > 2x - 1 = 0

= > 2x = 1

= > x = 1/2.

plug x = 1/2, we get

= > 2(1/2)^3 - (1/2)^2 + 3(1/2) - 1

= > 1/4 - 1/4 + 3/2 - 1

= > 3/2 - 1

= > 1/2.


Here remainder is 1/2. Therefore 2x - 1 is not a factor of 2x^3 - x^2 + 3x - 1.


Hope this helps!

Answer 2

if (2x - 1) is the factor, so remainder must be 0


By Remainder Theorem,

2x - 1 = 0 

2x = 1 

x = 1/2 



Then,

2x^3 - x^2 + 3x - 1 = 0 

2(1/2)^3 - (1/2)^2 + 3(1/2) - 1 = Remainder

2(1/8)  - (1/4) + 3/2 - 1 =  Remainder

1/4  - 1/4 + 3/2 - 1 = Remainder

3/2 - 1 = Remainder

(3 - 2)/2 = Remaider

1/2 = Remainder 




Hence, (2x -1) is not the factor of the given p(x) 
and Remainder = 1/2