Define a recursive function prefix that accepts a positive integer n and a list xs as input, and returns a list containing only the first n elements in xs. - This function must have a recursive definition and does not use any library functions!

F# Code:

let rec prefix n list =

//Extracting head and tail elements

let valHead = (Listhead list)

let valTail = (Listtail list)

// Checking n value

match n with

| 0 -> []

| _ -> [valHead] at (prefix (n-1) valTail) // Creating list recursively

//Testing function

let lstT = [1; 2; 3; 4; 5]

printfn "%A" (prefix 3 lstT)

printfn "%A" (prefix 2 lstT)

printfn "%A" (prefix 4 lstT)

Step-by-step explanation: see attachment below for sample run

(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