Answer:
2. Eunju is right
3. is a factor of
.
Step-by-step explanation:
<u>Polynomial Remainder Theorem</u>
The polynomial remainder theorem states that the remainder of the division of a polynomial f(x) by (x-a) is equal to f(a).
As a consequence, if a polynomial is divisible by x-a, f(a)=0.
Part 1:
Let's make:
To find out if x+b is a factor of f(x), we find f(-b):
Operating:
The value of f(-b) is not zero. This means Eunju is right, x+b is not a factor of f(x).
Part 2:
We must find out if is a factor of
without using long division or synthetic division.
We can use the polynomial remainder theorem again, but since the factor is not in the form (x-a), we can factor it as follows:
Now we just apply the theorem twice. If both remainders are zero, then the assumption is true.
Let's make:
Find f(-2):
Find f(-3):
Since both f(-2) and f(-3) are zero, is a factor of
.