Use the remainder theorem to find the value of f(x).
find f(3).
f(x) = -x^3+ 4x² – 2x

Using remainder value theorem, the value of f(3) is 3

Solution:

Given, function is

We have to find the value of f(3) by using remainder theorem.

Now, we have to divide f(x) with x – 3, because we want value of f(3)

If we want f(a), then we have to divide with x – a.

Now, first let us factorize the f(x)

Now, let us divide the f(x) with x – 3

Now, multiply f(x) with (x -3) ⇒ (-x(x -1) + 1)(x -3) + 3

This is in the form of:

Hence, the remainder is 3.

Therefore the value of f(3) is 3

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