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HELP!!! I got the first part done but I feel as though I did it wrong because I can't seem to get part 2 or 3 done.
Create a quadratic polynomial function f(x) and a linear binomial in the form (x − a).
f(x) = ax^2 + bx + c a = 1 b = 4 c = 6 (x – a) a = -2
f(x) = x^2 + 4x + 6 (x – 2)
Part 1. Show all work using long division to divide your polynomial by the binomial.
X + 4
x-2√(x^2+4x+6)
-x^2+2x
6x + 6
- 6x + 12 18 is the remainder of x + 4
18 x + 4 + 18/(x-2)
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

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Answer:

It's all below...

Step-by-step explanation:

Part 1.

quadratic poynomial function:   f(x)=x2−5x+6

linear binomial:   x−2

x−3x−2x2−5x+6x2−2x−−−−−−−−−−3x+6−3x+6−−−−−−−−0

Part 2.  

f(2)=22−5(2)+6=4−10+6=−6+6=0

Part 3.  


The remainder theorem says that if f(x) is divided by x-a, then f(a) will be the remainder. When we divided f(x) by x - 2 , we got a remainder of 0, which by the remainder theorem implies f(2) = 0.  That means x-2 is a factor of f(x).