Question

If f(x) = 2x² + 5, then what is the remainder when f(x) is divided by x + 3?

Answer 1

To find the remainder when f(x) = 2x² + 5 is divided by x + 3, use synthetic division to divide the polynomial and find the remainder.

Step-by-step explanation:

To find the remainder when f(x) = 2x² + 5 is divided by x + 3, we can use synthetic division. Synthetic division is a method used to divide a polynomial by a linear expression.

First, set up the synthetic division table with the divisor x + 3 and the coefficients of the polynomial f(x):

• | -3 | 2 | 0 | 5 |

Perform synthetic division. Bring down the first coefficient, multiply it by the divisor, and add it to the next coefficient. Repeat this process until the end of the polynomial:

• | -3 | 2 | 0 | 5 |
• -3| -6 | 12 | -12 |

The remainder is the last number in the synthetic division: -12. Therefore, the remainder when f(x) is divided by x + 3 is -12.