Question

find the remainder when f(x)=3x^4+2x^3-x^2/3-x/9+12/27 is divided by (x+2/3)​

Answer 1

Step-by-step explanation:

Let f(x) = 3x^4+2x^3-x^2/3-x/9+12/27

And the zero of (x+2/3)= -2/3

Therefore x= -2/3

So, f(-2/3)= 3(-2/3)^4 + 2(-2/3)^3-(2/3)^2/3(-2/3)/9+12/27

=> f(-2/3)= 3(-8/3)+2(-2)-(4/9)+(2/3)/9+12/27

=> f(-2/3)= -8-4-4/9+2^9/3+12/27

=> f(-2/3)= -8-4-4/9+18/3+12/27

=> f(-2/3)= -8-4-4/9+(162+12/27)

=> f(-2/3)= -8-4-4/9+174/27

=> f(-2/3)= -8-4(-12+174/27)

=> f(-2/3)= -8-4+162/27

=> f(-2/3)= -8+54/27

=> f(-2/3)= -162/27