Answer: To find the remainder when the polynomial 5x^2 + 10x - 15 is divided by x + 5, we can use polynomial long division or synthetic division. Here, we will use synthetic division:
The divisor is x + 5, so we change its sign and write -5 as the constant in the synthetic division setup. Then we list the coefficients of the terms of the dividend polynomial, in decreasing order of powers of x, and place a placeholder for the missing x term:
-5 | 5 0 10 -15
| -25 125 -675
+----------------
5 -25 135 -690
The remainder is the last number in the bottom row, which is -690. Therefore, the remainder when 5x^2 + 10x - 15 is divided by x + 5 is -690.
Explanation: