Final answer:
Synthetic division of the polynomial (x² + 3) by (x - 1) results in a quotient of x + 1 with a remainder of 4, which can be expressed as x + 1 plus 4/(x - 1).
Step-by-step explanation:
Solving Using Synthetic Division
To solve the division of the polynomial (x² + 3) by (x − 1) using synthetic division, we start by setting up the synthetic division table. First, write down the coefficients of the polynomial which in this case are 1 (for x²), 0 (since there is no x term), and 3. Next, write the zero of the divisor x-1, which is 1, to the left of the table.
We then bring down the leading coefficient to the bottom row. After that, multiply this coefficient by the zero of the divisor, and write the result in the next column of the second row. Then, add the numbers of the second and third rows to get the new number in the bottom of the second column, and repeat the multiplying and adding process until the table is complete.
The result of synthetic division gives us the quotient of the division process. In our case, the quotient will be x + 1 with a remainder of 4, meaning (x² + 3) ÷ (x − 1) equals x + 1 with a remainder of 4, or expressed as x + 1 + 4/(x - 1).