Final answer:
To find the quotients of each question, perform long division. In question A, divide x^4 by x to get x^3, then repeat until the end. In question B, divide x^5 by x to get x^4, then repeat until the end.
Step-by-step explanation:
To find the quotients of each question, you need to perform long division. Let's start with question A:
(x^4 + 4x + 45) divided by (x-3)
First, divide x^4 by x to get x^3. Then, multiply x-3 by x^3 to get x^4 - 3x^3. Subtract this result from the original polynomial to get 7x^3 + 45. Repeat the process with the remainder.
Now let's move on to question B:
(x^5 + 5x^3 + 12) divided by (x+3)
Similar to before, start by dividing x^5 by x to get x^4. Multiply x+3 by x^4 to get x^5 + 3x^4. Subtract this from the original polynomial to get 2x^4 + 5x^3 + 12. Repeat the process until you reach the end.