If  f(x)  =  x3 + x2 − ax + b  is divisible by  x2 − x , then the value of  a + b  = Select an answerA–2B0C2D6

The given polynomial f(x) = x^3 + x^2 - ax + b is divisible by x^2 - x.

This means that when we divide f(x) by x^2 - x, there should be no remainder.

We can write x^2 - x as x(x - 1).

So, the roots of the divisor are x = 0 and x = 1.

According to the Factor theorem, if a polynomial f(x) is divisible by x - a, then f(a) = 0.

So, we can say that f(0) = 0 and f(1) = 0.

Let's calculate these values:

f(0) = 0^3 + 0^2 - a*0 + b = b. Since f(0) = 0, we have b = 0.

f(1) = 1^3 + 1^2 - a*1 + b = 1 + 1 - a + 0 = 2 - a. Since f(1) = 0, we have 2 - a = 0, which gives a = 2.

So, a + b = 2 + 0 = 2.

Therefore, the correct answer is C. 2.