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

Factorize each of the following quadratic polynomials by using the method of completing the square:
4x2 − 12x + 5

Solution:

$4 x^{2}-12 x+5$

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

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

$=4\left[\left(x-\frac{3}{2}\right)^{2}-\frac{9}{4}+\frac{5}{4}\right] \quad[$ Completing the square $]$

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

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

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

$=4\left(x-\frac{5}{2}\right)\left(x-\frac{1}{2}\right)$

$=(2 x-5)(2 x-1)$

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