Question # 01: Find the square root of the following polynomials by factorization method:
\((i)\) \(\;\) \( x^2-8x+16\)
Solution:
$=x^{2} -8x+16$
$=x^{2} -2( x)( 4) +4^{2}$
$\displaystyle =( x-4)^{2}$
Taking square root, we have
$ $$\sqrt{x^{2} -8x+16} =\pm \sqrt{( x-4)^{2}}$
$\displaystyle \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =\pm ( x-4)$
——– Alternate Method ——–
$=x^{2} -8x+16$
$=x^{2} -4x-4x+16$
$=x( x -4) -4( x-4)$
$=( x-4)( x-4)$
$\displaystyle =( x-4)^{2}$
Taking square root, we have
$ $$\sqrt{x^{2} -8x+16} =\pm \sqrt{( x-4)^{2}}$
$\displaystyle \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =\pm ( x-4)$