# Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial, write and factor the trinomial. x^2−3x.

Polynomials
Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial, write and factor the trinomial.
$$\displaystyle{x}^{{2}}−{3}{x}.$$

The coefficient of the x-term in "$$\displaystyle{x}^{{2}}–{3}{x}$$" is “-3”
Half of “-3” is $$\displaystyle-\frac{{3}}{{2}}{\quad\text{and}\quad}{\left(-\frac{{3}}{{2}}\right)}^{{2}}=\frac{{9}}{{4}}$$, then
$$\displaystyle{x}^{{2}}–{3}{x}+\frac{{9}}{{4}}={\left({x}–\frac{{3}}{{2}}\right)}^{{2}}$$
The answer is $$\displaystyle\frac{{9}}{{4}},{\left({x}–\frac{{3}}{{2}}\right)}^{{2}}$$