Question # 01: Find the square root of the following polynomials by factorization method:
\((vi)\) \(\; \) \(40x^2+120x+90\)
Solution:
$=40x^{2} +120x+90$
$=10\left[ 4x^{2} +12t+9\right]$
$=10\left[( 2x)^{2} +2( 2x)( 3) +3^{2}\right]$
$\displaystyle =10( 2x+3)^{2}$
Taking square root, we have
$ $$\sqrt{40x^{2} +120x+90} =\pm \sqrt{10( 2x+3)^{2}}$
$\displaystyle \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =\pm \sqrt{10}( 2x+3)$