Task 5—Polynomial Division and the Remainder Theorem Create a quadratic polynomial function f(x) and a linear binomial in the form (x − a).

Part 1. Show all work using long division to divide your polynomial by the binomial.

Part 2. Show all work to evaluate f(a) using the function you created.

Part 3. Use complete sentences to explain how the remainder theorem is used to determine whether your linear binomial is a factor of your polynomial function

See Explanation

Step-by-step explanation:

Let our quadratic polynomial function

Let our linear binomial in the form (x − a)=x-1

Part 1: We use long division to divide the polynomial by the binomial.

Therefore:

Part 2: In our chosen linear monomial x-1, a=1

Part 3:

To determine whether a linear binomial is a factor of a polynomial function using the remainder theorem

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.