Final answer:
To find the remainder when f(x) is divided by x-6, substitute x-6 into f(x)=5x^2+3 and evaluate it. The remainder is
5x^2 - 60x + 183.
Step-by-step explanation:
To find the remainder when f(x) is divided by x-6, we can use the remainder theorem.
According to the remainder theorem, if we substitute the divisor x-6 into f(x) and evaluate it, the result will be the remainder.
So, substituting x-6 into f(x)=5x^2+3, we get:
f(x-6) = 5(x-6)^2 + 3
To simplify further, we can expand the binomial term:
f(x-6) = 5(x^2 - 12x + 36) + 3
Now, distribute the 5:
f(x-6) = 5x^2 - 60x + 180 + 3
Combine like terms:
f(x-6) = 5x^2 - 60x + 183
Therefore, the remainder when f(x) is divided by x-6 is 5x^2 - 60x + 183.