Question

Factorise the following trinomials:
$x^2+5x+\frac{25}{4}$

Answer 1

$x^2+5x+\frac{25}{4}$

$=x^2+\frac{5}{2}x+\frac{5}{2}x+\frac{25}{4}$

$=x(x+\frac{5}{2})+\frac{5}{2}(x+\frac{5}{2})$

$=(x+\frac{5}{2})(x+\frac{5}{2})$

Hence the factors of $x^2+5x+\frac{25}{4}$ are $(x+\frac{5}{2})$ and $(x+\frac{5}{2})$.