Resolve each of the following quadratic trinomial into factor:

The given expression is $11 \mathrm{x}^{2}-54 \mathrm{x}+63 .      \quad$ (Coefficient of $\mathrm{x}^{2}=11$, coefficient of $\mathrm{x}=-54$ and constant term $=63$ )

We will split the coefficient of $\mathrm{x}$ into two parts such that their sum is $-54$ and their product equals the product of the coefficient of $\mathrm{x}^{2}$ and the constant term, i.e., $11 \times 63=693$.

Now,

$(-33)+(-21)=-54$

and

$(-33) \times(-21)=693$

Replacing the middle term $-54 \mathrm{x}$ by $-33 \mathrm{x}-21 \mathrm{x}$, we have :

$11 \mathrm{x}^{2}-54 \mathrm{x}+63=11 \mathrm{x}^{2}-33 \mathrm{x}-21 \mathrm{x}+63$

$=\left(11 \mathrm{x}^{2}-33 \mathrm{x}\right)+(-21 \mathrm{x}+63)$

$=11 \mathrm{x}(\mathrm{x}-3)-21(\mathrm{x}-3)$

$=(11 \mathrm{x}-21)(\mathrm{x}-3)$