Question

What number should be added to the expression x^2+3x+___ in order to create a perfect square trinomial?

Answer 1

Answer:  THIRD OPTION.

Step-by-step explanation:

We need to remember that we can create a perfect square trinomial by squaring a binomial:

$(a\±b)^2=a^2\±2ab+b^2$

Then we need need to pick the coefficient of the x term of the given expression, divide it by 2 and square it:

$(\frac{3}{2})^2=\frac{9}{4}$

Therefore, the number that should be added to the given expression  in order to create a perfect square trinomial is:

$\frac{9}{4}$