The quotient and remainder for the last row of the synthetic division 3, 0, 4, 0, 1 are 3x³ + 4x, and 1 respectively.
The option representing this is, a. 3x³ + 4x R1.
What is synthetic division?
Synthetic division is a short method of dividing a polynomial p(x) by another polynomial (x - c), to get the quotient and remainder.
The last row represents the quotient and remainder, the last digit being the remainder, and the others being the quotient multiplied by leading powers of x, starting from x⁰, starting from the second last term of the last row.
How to solve the question?
In the question, we are given the last row of a synthetic division as 3, 0, 4, 0, 1, and we are asked to find the quotient of the division.
The last number, 1 represents the remainder and can be written as R1.
Now we move from the back to the front and multiply every number with the leading power of x, starting from x⁰.
- 0 gives 0 * x⁰ = 0
- 4 gives 4 * x¹ = 4x
- 0 gives 0 * x² = 0
- 3 gives 3 * x³ = 3x³.
Therefore, the quotient and remainder for the last row of the synthetic division 3, 0, 4, 0, 1 are 3x³ + 4x, and 1 respectively.
The option representing this is, a. 3x³ + 4x R1.
Learn more about the Synthetic Division at
https://brainly.com/question/24662212
#SPJ2
