I WILL GIVE BRAINLIEST IF YOU CAN ANSWER THESE TWO QUESTIONS 2. Darwin believes that x + b is a factor of (x + b)3 + (x + c)2 – (b - c), while Eunju
believes it is not. Who is correct? Justify your response.

3. How can you prove that x2 + 5x + 6 is a factor of x* + 5x3 + 2x2 – 20x – 24, without
using long or synthetic division?

2. Eunju is right

3. is a factor of .

Step-by-step explanation:

Polynomial Remainder Theorem

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 .

the answer is n

last one.

step-by-step explanation:

last one.

generally speaking, the others follow some sort of pattern that correlates to either linear (looks like a straight line) or sinusoidal (looks like an s).

the last one is just a random cloud of points that doesn't correlate to any particular known order.