Factorize each of the following quadratic polynomials by using the method of completing the square:

$4 y^{2}+12 y+5$

$=4\left(y^{2}+3 y+\frac{5}{4}\right) \quad\left[\right.$ Making the coefficient of $\left.y^{2}=1\right]$

$=4\left[y^{2}+3 y+\left(\frac{3}{2}\right)^{2}-\left(\frac{3}{2}\right)^{2}+\frac{5}{4}\right] \quad\left[\right.$ Adding and subtracting $\left.\left(\frac{3}{2}\right)^{2}\right]$

$=4\left[\left(y+\frac{3}{2}\right)^{2}-\frac{9}{4}+\frac{5}{4}\right]$

$=4\left[\left(y+\frac{3}{2}\right)^{2}-1^{2}\right] \quad[$ Completing the square $]$

$=4\left[\left(y+\frac{3}{2}\right)-1\right]\left[\left(y+\frac{3}{2}\right)+1\right]$

$=4\left(y+\frac{3}{2}-1\right)\left(y+\frac{3}{2}+1\right)$

$=4\left(y+\frac{1}{2}\right)\left(y+\frac{5}{2}\right)$

$=(2 y+1)(2 y+5)$