Answer:
Quotient is and remainder is 0.
Step-by-step explanation:
Given:
Dividend =
Divisor =
The long division is shown in the attachment.
Step 1: we need to divide with
we first multiply
with 3x we get the remainder as
Quotient as 3x.
Step 2: Now the dividend is and divisor
now we will multiply
with -5 we get the remainder as 0 and Quotient as
Hence Quotient is and remainder is 0.
Answer:
b.
Step-by-step explanation:
We have to look at sign changes in f(x) to determine the possible positive real roots.
There is only one sign change here, between the -8x and the +4. So that means there is only 1 possible real positive root.
Now we have to look at sign changes in f(-x) to determine the possible negative real roots.
There are 3 sign changes here. That means there are either 3 negative roots or 3-2 = 1 negative root. So we have:
1 positive
3 or 1 negative
We need to pair them up now with all the possible combinations.
If we have 1 positive and 1 negative, we have to have 2 imaginary
If we have 1 positive and 3 negative, we have to have 0 imaginary
Keep in mind that the total number or roots--positive, negative, imaginary--have to add up to equal the degree of the polynomial. This is a 4th degree polynomial, so we will have 4 roots.