Question

Which constant should be added to the binomial x^2-10x so that it becomes a perfect square trinomial? A. 5B. 10C. 100D. 25

Answer 1

$x^2-10x$

A perfect square trinomial has the next general form:

$a^2-2ab+b^2=(a-b)^2$

The term 2ab in the given equation is: 10x or 2(5)x

Then:

$\begin{gathered} 2ab=2\cdot5x \\ 2=2 \\ a=x \\ b=5 \end{gathered}$

Then, to becomes the given binomial into a perfect sqare trinomial you add b squared, you get:

$\begin{gathered} x^2-10x+5^2 \\ x-10x+25 \end{gathered}$Then, the constant you add is 25