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The G. C. D. of $(x^{2} - 3 x + 2), (x^{2} - 4 x + 4)$ is :

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(x - 2)

(x - 2) (x - 1)

{(x - 2)}^{2}

{(x - 2)}^{3} (x - 1)

answer is A.

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Detailed Solution

Concept: First factorise both the polynomials and write their factors and then take the factors common in both polynomials as their G. C. D.
For a given polynomial of the form,

x^{2} - (a + b) x + ab

then we factorise as

(x - a) (x - b)

We will factorise the polynomials separately
First polynomial

(x^{2} - 3 x + 2)

, we see that

a + b = 3, ab = 2

Now we’ll take numbers having sum as 3 and multiplication as 2.

(x^{2} - 3 + 2) = (x - 1) (x - 2)

-(i)
Similarly for second polynomial,

(x^{2} - 4 x + 4)

, we see that

a + b = 4, ab = 4

Take numbers having sum as 4 and multiplication as 4.

(x^{2} - 4 x + 4) = (x - 2) (x - 2)

-(ii)
From eq. (i) & eq. (ii) , we get

(x - 2)

as a common factor of both the polynomials.
Therefore, G. C. D. of these polynomials is

(x - 2)

G. C. D. of

(x^{2} - 3 x + 2)

and

(x^{2} - 4 x + 4)

(x - 2)

.
Hence, the correct option is (1).

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