Question

Use synthetic division to solve (3x⁴ + 6x³ + 2x² + 9x + 10) / (x - 2). What is the quotient?

Answer 1

To find the quotient of (3x⁴ + 6x³ + 2x² + 9x + 10) divided by (x - 2) using synthetic division, write down the coefficients of the polynomial, use 2 (the zero of x - 2) to perform the division, and follow the multiply-add process until all coefficients are processed. The numbers at the bottom row represent the coefficients of the quotient.

Step-by-step explanation:

To find the quotient of (3x⁴ + 6x³ + 2x² + 9x + 10) divided by (x - 2) using synthetic division, write down the coefficients of the polynomial, use 2 (the zero of x - 2) to perform the division, and follow the multiply-add process until all coefficients are processed. The numbers at the bottom row represent the coefficients of the quotient.

To use synthetic division to divide (3x⁴ + 6x³ + 2x² + 9x + 10) by (x - 2) and find the quotient, we follow these steps:

1. Write down the coefficients of the polynomial: 3, 6, 2, 9, 10.
2. Write down the zero of the divisor x - 2, which is 2.
3. Bring down the first coefficient (3) to the bottom line.
4. Multiply this number by the zero of the divisor (2), and write the result below the second coefficient. Add this result to the second coefficient and write the sum below.
5. Repeat the multiplication and addition process until you reach the end of the coefficients.
6. The numbers at the bottom are the coefficients of the quotient.

The quotient of the synthetic division would be a third-degree polynomial with its new set of coefficients.