Question

"Let's say you have a polynomial function

f(x) = 4x^4 - 3x^2 - 52
and have the three divisors of:
(x + 2)
(x + 3)
(x-2)
What are remainders and which of these divisors are factors based on those remainders?"
A. Remainder when dividing by (x + 2): 0
B. Remainder when dividing by (x + 3): 0
C. Remainder when dividing by (x - 2): 0
D. All three divisors are factors.

Answer 1

The remainders when dividing the polynomial function by each of the provided divisors are zero, indicating that all three divisors are factors of the polynomial.

Step-by-step explanation:

To determine if the divisors (x + 2), (x + 3), and (x - 2) are factors of the given polynomial function, we need to check if the remainders are zero when dividing by each of these divisors.

1. Remainder when dividing by (x + 2): 0
2. Since the remainder is zero, (x + 2) is a factor of the polynomial.
3. Remainder when dividing by (x + 3): 0
4. Since the remainder is zero, (x + 3) is a factor of the polynomial.
5. Remainder when dividing by (x - 2): 0
6. Since the remainder is zero, (x - 2) is a factor of the polynomial.

Therefore, all three divisors are factors of the polynomial.