Question

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

Answer 1

$$\begin{gathered} 4x^2-12x+5 \\ =4(x^2-3x+\frac{5}{4})[Makingthecoefficientof{x}^2=1] \\ =4[x^2-3x+{\left(\frac{3}{2}\right)}^2-{\left(\frac{3}{2}\right)}^2+\frac{5}{4}][Addingandsubtracting{\left(\frac{3}{2}\right)}^2] \\ =4\left[\right(x-\frac{3}{2}{)}^2-\frac{9}{4}+\frac{5}{4}][Completingthesquare] \\ =4[(x-\frac{3}{2}{)}^2-1^2] \\ =4\left[\right(x-\frac{3}{2})-1]\left[\right(x-\frac{3}{2})+1] \\ =4(x-\frac{3}{2}-1)(x-\frac{3}{2}+1) \\ =4(x-\frac{5}{2})(x-\frac{1}{2}) \\ =(2x-5)(2x-1) \end{gathered}$$