# 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.

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

2020-12-26
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 $$\displaystyle\frac{{9}}{{4}},{\left({x}–\frac{{3}}{{2}}\right)}^{{2}}$$

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