If x - 2 is a factor of the polynomial x2 + ax + 2b and a + b = -2, then the values of a and b will be:

Explanation -

If x - 2 is a factor of the polynomial x² + ax + 2b, it means that when x = 2 is substituted into the polynomial, the result should be zero. 

Let's substitute x = 2 into the polynomial x² + ax + 2b and set it to zero:

Given polynomial: x² + ax + 2b

Substituting x = 2:
\((2)^2 + a(2) + 2b = 0\\ 4 + 2a + 2b = 0\\ 2a + 2b = -4\\ a + b = -2 \)

We also have the given condition that a + b = -2.

Hence both the equations are same so we want to find the value of a and b from the given options.

(1) a = -1, b = -3

a + b = -1 +(-3) = -1 -3 = -4

So false.

(2) a = 1, b = 3

a + b = 1 + 3 = 1 + 3 = 4

So false.

(3) a = -3, b = 1

a + b = 1 + (- 3) = 1 - 3 = -2

So true.

(4) a = 5, b = -3

a + b = 5 + (- 3) = 5 - 3 = 2

So false.

Hence the correct answer is a = -3, b = 1.