Can someone please help?

Question

 

 

𝑓(𝑥) = 𝑥2 − 7𝑥 + 4 𝑎𝑛𝑑 𝑐 = 2
a. Evaluate 𝑓(𝑐) directly

b. Evaluate 𝑓(𝑐) using the Synthetic division and the Remainder Theorem.

Answer 1

a. f(x)=x²-7x+4 --->f(c)=c²-7c+4

   Replace c with 2 and solve.

   f(2)=2²-7(2)+4

        =4-14+4

        =-6

b. The Remainder Theorem states that a polynomial, f(x), divided by a binomial, x-a, is the constant remainder, f(a).

    That is:  Dividend equals quotient times divisor plus remainder. Using synthetic division, we need to divide x²-7x+4 by

    x-2. Because c=2 we need to do this:

                           2  1  -7  4    

                                    2 -10

                               1  -5  -6<---This is your remainder which is your answer to f(c).

*Notice that both answers are the same, -6.

 

Answer 2

𝑓(𝑥) = 𝑥² − 7𝑥 + 4 𝑎𝑛𝑑 𝑐 = 2

 

Evaluate directly:

 

f(c) = f(2) = 2² - 7·2 + 4 = 4 - 14 + 4 = -6

 

Evaluate via Synthetic division and the Remainder Theorem.  Divide x²-7x+4 by x-2.  The remainder will equal f(c=2):

 

2 |  1   -7    4

      ↓    2  -10

    -------------

      1  -5   -6

 

The remainder is the last term in the quotient, -6, so (f(c=2) = -6