Answer:
Step-by-step explanation:
What you are looking for is the simplification of f(x) divided by g(x). This can be easily accomplished with synthetic division. If we are dividig the quadratic by x - 1, we will use the fact that if x - 1 = 0, then x = 1. We will put that 1 outside the "box" and put the coefficients from the quadratic inside the "box" and do the division synthetically. The coefficients on the quadratic terms are 2, 1, and -3:
1 | 2 1 -3
___________
We begin by bringing down the first number, a 2, and multiplying it by the 1 in the box and putting the product up under the 1:
1 | 2 1 -3
2
2
Now we add down the column:
1 | 2 1 -3
2
2 3
Now multiply the 3 by the 1 outside the box and put that product up under the -3 and then add down that column:
1 | 2 1 -3
2 3
2 3 0
Because we have a 0 remainder, that means that the quadratic was evenly divisible by x - 1. What we have left is called a depressed polynomial. It takes on the x values at one degree lesser than what we started with. Namely, it will be 2x + 3.
2x + 3 is what we get when we divide the quadratic by x - 1. BUT because we started off with x - 1 in the denominator, even though we divided it away to simplify, we still have to take into account that the value of 1 makes the denomiator go to 0, which is never allowed in math.
So the answer you want is the first one!
