Question

Use synthetic division to solve (x3 1) ÷ (x – 1). What is the quotient? x squared x 1 StartFraction 2 Over x 1 EndFraction x squared minus x 1 x squared x 1 StartFraction 2 Over x minus 1 EndFraction x cubed minus x squared x minus 1.

Answer 1

When dividing (x^3 + 1) by (x - 1) using synthetic division, the quotient is x^2 + x + 1, obtained by applying synthetic division steps to the polynomial's coefficients.

Step-by-step explanation:

To solve the division (x3 + 1) ÷ (x - 1) using synthetic division, we write down the coefficients of the polynomial we are dividing: 1 (for x3), 0 (for x2 since it is missing in the polynomial), 0 (for x, also missing), and 1 (the constant term). Next, we use 1 as the divisor (since we are dividing by x - 1), and apply synthetic division:

• Bring down the leading coefficient (1).
• Multiply by the divisor (1) and write the result below the next coefficient.
• Add down the column.
• Repeat these steps until all coefficients have been used.

The final result of the synthetic division will give us the coefficients of the quotient. For (x3 + 1), dividing by (x - 1), the quotient using synthetic division is x2 + x + 1, with no remainder.