.
There is MUCH SIMPLER WAY to get the answer.
Notice, that the remainder of dividing the given polynomial by binomial (x+2) is a constant term.
Use the Remainder theorem: the remainder of division of any polynomial f(x) by a binomial (x-a) is equal
to the value f(a) of the polynomial at x= a:
In your case, the remainder of division of the given polynomial f(x) = -3x^3-4 by (x+2) is equal to
f(-2) = -3*(-2)^3-4 = -3*(-8)-4 = 24-4 = 20. ANSWER
Solved.
By using this method, you do not need to perform division (!)
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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.
