Question

If f (x) = x3 + ax + b is divisible by (x - 1)2, then the remainder obtained when f (x) is divided by (x + 2) is:

Answer 1

Answer:

Step-by-step explanation:

Here's a quick way:

The function is a polynomial of third degree, so there are exactly three roots, when counting with multiplicity.

Since the polynomial is divisible by (x-1)^2, it has x=1 as a double root. So two of the three roots are 1.

Now, the coefficient in front of x^2 is related to the sum of all three roots. Since there is no term with x^2, it means that the sum of all three roots is zero. Since two roots have a value of 1, the last remaining root must have the value -2. Hence the function is divisble by (x+2). Therefore, the remainder is zero.

Answer 2

Answer is zero

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Step-by-step explanation: