.
In accordance with the Remainder theorem, it is enough to check if
(1) the number -2 is the root of the first polynomial:
indeed, = -32 + 32 = 0;
so, -2 is the root; hence the polynomial is divisible by (x+2).
(2) the number is the root of the second polynomial:
indeed, - = - = 0;
so, is the root; hence the polynomial is divisible by .
The ANSWER is "YES" in both cases.
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Theorem (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 lessons
- Divisibility of polynomial f(x) by binomial x-a and the Remainder theorem
- Solved problems on the Remainder thoerem
in this site.
Also, you have this free of charge online textbook in ALGEBRA-II in this site
ALGEBRA-II - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic
"Divisibility of polynomial f(x) by binomial (x-a). The Remainder theorem".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.