Question

State if the following are perfect square trinomials. Show work that proves your conclusion.

Answer 1

A quadratic expression is said to be a perfect square trinomial if it has repeated factors.

Given the expression below:

`x^2+7x+(49)/(4)`

By factorization, we have

`\begin{gathered} (x^2+(7)/(2)x)+((7)/(2)x+(49)/(4)) \\ factor\text{ out the common term,} \\ x(x+(7)/(2))+(7)/(2)(x+(7)/(2)) \\ This\text{ gives} \\ (x+(7)/(2))(x+(7)/(2)) \\ \Rightarrow(x+(7)/(2))^2 \\ \end{gathered}`

Since the above expression has a repeated factor of

`(x+(7)/(2))`

We can conclude that the expression is a perfect square trinomial.