Question

(5x³ 4x²-31x 6) / (x 2) synthetic division?

Answer 1

Synthetic division is used to divide the polynomial (5x³ + 4x² - 31x + 6) by the binomial (x + 2), resulting in a quotient polynomial of 5x² - 6x - 19 with a remainder of 32.

Step-by-step explanation:

The question asks for the synthetic division of the polynomial (5x³ + 4x² - 31x + 6) by the binomial (x + 2). To perform synthetic division, we follow these steps:

1. Write down the coefficients of the polynomial: 5, 4, -31, 6.
2. Write the zero of the binomial (x + 2) which is -2 to the left of the division symbol.
3. Bring down the first coefficient (5).
4. Multiply the zero (-2) by the new number (5) and write the result below the next coefficient (4).
5. Add the column: 4 + (-10) = -6.
6. Repeat the multiplication and addition process until you have processed all coefficients.
7. The result will be the coefficients of the quotient polynomial.

Performing these steps, we find the quotient polynomial has coefficients that form the polynomial 5x² - 6x - 19 with a remainder of 32.