Question

Find the remainder when f(x)=x*4-3x*2+4 is divided by g (x)=x-2 and verify result by actual division

Answer 1

Verification...

= (x - 2)( {x}^{3}  + 2 {x}^{2}  + x + 2) + 8 \\  =  {x}^{4}  + 2 {x}^{3} +  {x}^{2}   + 2x - 2 {x}^{3}  - 4 {x}^{2} - 2x - 4 + 8 \\  = x {}^{4}   - 3 {x}^{2}  + 4

Hope it helps....

Answer 2

f (x) is x^4 - 3x^2 + 4

g (x) is x - 2

f (x) = (2)^4 - 3 (2)^2 + 4

= 16 - 2 + 4

= 8