If f(x + 2) = f(x) + f(2) then prove that: f(0) = 0 and f(-2) = -f(2)

f(0)=0,

f(-2)=-f(2)

Step-by-step explanation:

f(x+2)=f(x)+f(2)

1. x=0

f(0+2)=f(0)+f(2)

f(2)=f(0)+f(2)

f(0)=f(2)-f(2)=0

f(0)=0

2. x=-2

f(-2+2)=f(-2)+f(2)

f(0)=f(-2)+f(2)

f(0)=0, f(-2)+f(2)=0

f(-2)=-f(2)

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0