Question

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
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asked 2020-12-25
Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial, write and factor the trinomial.
\(\displaystyle{x}^{{2}}−{3}{x}.\)

Answers (1)

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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