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Example 4. (x² + x - 2) is the G.D.C. of the expression (x - 1) (2x² + ax + 2) and (x + 2) (3x² + bx + 1). Find the value of a and b.

Solution:- x² + x - 2 = (x + 2) (x - 1)

Let P(x) = (x - 1) (2x² + ax + 2)

and Q(x) = (x + 2) (3x² + bx + 1)

Let us take P(x), here we find that x + 2 is a factor of 2x² + ax + 2.

i.e. 2( -2)² + a(-2) + 2 = 0

or, -2a + 10 = 0

a = 5

Similarly x - 1 is a factor of 3x² + bx + 1

3(1)² + b.1 + 1 = 0

b = -4

a = 5, b = -4.