Final answer:
To find the remainder when a function is divided by x-2, substitute x=2 into the function.
Step-by-step explanation:
To find the remainder when a function is divided by x-2, we can use the Remainder Theorem. The Remainder Theorem states that if we divide a polynomial f(x) by x-a, the remainder will be f(a).
In this case, we have f(x) = 4x³-5x²+7x+10 and we want to find the remainder when f(x) is divided by x-2.
To find the remainder, we can substitute x=2 into the polynomial f(x) and compute the value:
f(2) = 4(2)³-5(2)²+7(2)+10 = 32-20+14+10 = 36.
So the remainder when f(x) is divided by x-2 is 36.