Question

Which of the following is/are the factor(s) of

$(x-2y{)}^2-5(x-2y)+6$

• A. $(x-2y-2)$
• B. (x−2y+3)
• C. $(x-2y-3)$
• D. (x+2y+3)

Answer 1

Answer: (A), (C)

The correct options are
A

$(x-2y-2)$

C

$(x-2y-3)$

$(x-2y{)}^2-5(x-2y)+6$

Let $(x-2y)=k$

$\Rightarrow k^2-5k+6$

$\Rightarrow k^2-2k-3k+6$

$\Rightarrow k(k-2)-3(k-2)$

$\Rightarrow (k-2)(k-3)$

Substituting the value of k, we get

$(x-2y-2)(x-2y-3)$