When the function f, of, xf(x) is divided by x, plus, 8x+8, the quotient is x^2plus, 3, x, minus, 3 and the remainder is 8.Find the function f, of, xf(x) and write the result in standard form.

Answer 1

To find the function f(x) given the quotient and remainder when f(x) is divided by x+8, we can set up the following division:

f(x) = (x^2 + 3x - 3)(x + 8) + 8

Expanding the right side of the equation:

f(x) = x^3 + 8x^2 + 3x^2 + 24x - 3x - 24 + 8

Simplifying further:

f(x) = x^3 + 11x^2 + 21x - 16

Therefore, the function f(x) is:

f(x) = x^3 + 11x^2 + 21x - 16