Question

to divide a function f(x+3) by (x^2+2x-3), we see the quotient is Q(x) and remainder is (x+2). If f(0)=a and f(4)=b, what is the value of (a+b)

a)2
b)4
c)8
d)10
e) none of the above

Answer 1

I divided the x+3 by the other polynomial.

What I did was factor the denominator to (x+3)(x-1)
The x+3 cancels with the one in the denominator
I was left with 1/(x-1)
f(0) would give me -1 and f(4) would give me 1/3 so I have none of the above.

If I didn't understand what you meant above... then maybe we are dividing (x+3) into the other polynomial. If that is the case.. we are left with x -1

f(0)= -1 and f(4)= 3 so the answer is 2... I think this is more likely what you were supposed to do.

Answer 2

You said:

f(x+3) / (x^2+2x-3) = Q(x) + (x+2)/(x^2+2x-3)
f(x+3) = (x^2+2x-3)Q(x) + x+2

we want f(0), so our x+3 = 0 or x = -3
f(0) = (9 - 6 - 3)Q(-3) + -3+2 = a
a = -1
we also want f(4), so our x+3 = 4, which means x = 1
f(4) = (1 + 2 - 3)Q(1) + 1+2 = b
b = 3

so
a+b = -1+3 = 2

Answer 3

Hey anyone help me on my post? In newest? Pls quick

Answer 4

[AI-generated answer — Explain Bot]

To find the value of (a+b), we need to evaluate the function f(x) and substitute the given values f(0) = a and f(4) = b.

Let's start by dividing the function f(x+3) by (x^2+2x-3) and finding the quotient Q(x) and remainder (x+2).

To divide f(x+3) by (x^2+2x-3), we can do the following steps:

Step 1: Rewrite f(x+3) as f(x) by substituting x+3 with x in the function f(x+3).
Step 2: Perform long division using f(x) and (x^2+2x-3).
Step 3: Write the quotient as Q(x) and the remainder as (x+2).

Now let's evaluate the function f(x) using the given values f(0) = a and f(4) = b.

Step 4: Substitute x = 0 in Q(x) and add the remainder (x+2). This gives us the value of f(0).
Step 5: Substitute x = 4 in Q(x) and add the remainder (x+2). This gives us the value of f(4).

Finally, we can calculate (a+b) by adding the values of f(0) and f(4).

Since the options provided do not give the actual numerical values of (a+b), we cannot directly determine the answer (a+b) from the given options. We would need to go through the steps described above to find the value of (a+b) based on the specific function f(x+3) and the values of f(0) and f(4) that are not given in the question.