Final answer:
The remainder when f(x) = 2x^2 - 5 is divided by x - 10 is 2x^2 - 40x + 195.
Step-by-step explanation:
To find the remainder when f(x) = 2x^2 - 5 is divided by x - 10, we can use the remainder theorem. According to the remainder theorem, if you substitute the divisor into the polynomial and evaluate it, you will get the remainder. So, substituting x - 10 into f(x), we get:
f(x) = 2(x - 10)^2 - 5
Expanding this equation gives:
f(x) = 2(x^2 - 20x + 100) - 5
f(x) = 2x^2 - 40x + 200 - 5
f(x) = 2x^2 - 40x + 195
This is the remainder when f(x) is divided by x - 10.