Question

determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. then, write and factor the trinomial.\\(x^2 + 18x\\)\\(\dots\\)\
what is the constant that should be added to the binomial so that it becomes a perfect square trinomial?

Explanation:

Step1: Identify linear term coefficient

The linear term is $18x$, so its coefficient is $18$.

Step2: Half the coefficient

$\frac{18}{2} = 9$

Step3: Square the result

$9^2 = 81$

Step4: Form perfect square trinomial

Add the constant to the binomial: $x^2 + 18x + 81$

Step5: Factor the trinomial

This factors to $(x + 9)^2$

Answer:

The constant to add is $81$, and the factored perfect square trinomial is $(x + 9)^2$.