Question

When the function f(x) is divided by x-1, the quotient is 1x^2+x-8 and the remainder is -2. Find the function f(x) and write the result in standard form.

Answer 1

Answer: When a polynomial is divided by x-1, the quotient is of the form of ax^2 + bx + c and the remainder is of the form of r. The quotient and the remainder are related by the formula:

f(x) = (x-1)(ax^2 + bx + c) + r

Given that the quotient is 1x^2+x-8 and the remainder is -2, we can substitute these into the above equation:

f(x) = (x-1)(1x^2+x-8) + (-2)

f(x) = x^3 - 9x^2 + (1-8)x +(-2)

f(x) = x^3 - 9x^2 - 7x - 2

Therefore the function f(x) is x^3 - 9x^2 - 7x - 2 in standard form.

Explanation: