Question

What value should be added to the expression to create a perfect square? x2 – 10x A. 25 B. –100 C. 5 D. 100

Answer 1

It's important to understand how perfect square trinomials work.

Say we had a factored perfect square trinomial in the form (x - n)²

If we distributed that out we'd have x² + 2nx + n².

Now, take a look at our expression... x² - 10x.
Imagine that 2nx term as 10x...n =5.
In that case, we'd have to add 25 to make our perfect square trinomial

as a rule of thumb: halve the x coefficient, square it, and then add it.