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. .
