.
The fact that (x-2) is a factor of means that the polynomial
p(x) =
has the root x= 2 (the Remainder theorem).
In other words, p(2) = = 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 by the binomial is equal to the value of the polynomial.
2. The binomial divides the polynomial if and only if the value of is the root of the polynomial , i.e. .
3. The binomial factors the polynomial if and only if the value of is the root of the polynomial , i.e. .
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".