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Example 3. (x - k) Is the g.c.d. of x² + x - 12 and 2x² - kx - 9. Find the value of k.

Solution:- Let P(x) = x² + x - 12 and Q(x) = 2x² - kx - 9

is the GCD. is

factor of P(x) and Q(x)

Putting x = k in P(x) we get

Putting x = k in Q(x) we get

from (i) and (ii) we get k = 3.