SOLUTION: x-2 is a factor of x^2 -ax-8, what's the value of a? A)2 B)4 C)-4 D)-2

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Question 1088877: x-2 is a factor of x^2 -ax-8, what's the value of a?
A)2
B)4
C)-4
D)-2
Answer by ikleyn(52858) About Me  (Show Source):
You can put this solution on YOUR website!
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The fact that (x-2) is a factor of x%5E2+-+ax+-+8 means that the polynomial

p(x) = x%5E2+-+ax+-+8

has the root  x= 2  (the Remainder theorem).


In other words,  p(2) = 2%5E2+-+a%2Ax+-8 = 0.


It implies  4 - 2a - 8 = 0,  2a = 4 - 8 = -4,  a = -2.


Answer.  a = -2.  Option D).


The remainder theorem: 
    1. The remainder of division the polynomial  f%28x%29  by the binomial  x-a  is equal to the value  f%28a%29  of the polynomial. 

    2. The binomial  x-a  divides the polynomial  f%28x%29  if and only if the value of  a  is the root of the polynomial  f%28x%29,  i.e.  f%28a%29+=+0.

    3. The binomial  x-a  factors the polynomial  f%28x%29  if and only if the value of  a  is the root of the polynomial  f%28x%29,  i.e.  f%28a%29+=+0.


See the lesson
    - Divisibility of polynomial f(x) by binomial (x-a) and the Remainder theorem
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic
"Divisibility of polynomial f(x) by binomial (x-a). The Remainder theorem".