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.
$x^2 + 8x$
what is the constant that should be added to the binomial so that it becomes a perfect square trinomial?

Explanation:

Step1: Identify coefficient of x

The coefficient of $x$ is $8$.

Step2: Half the coefficient

$\frac{8}{2} = 4$

Step3: Square the result

$4^2 = 16$

Step4: Write the trinomial

$x^2 + 8x + 16$

Step5: Factor the trinomial

A perfect square trinomial $x^2+2ax+a^2$ factors to $(x+a)^2$. Here $a=4$, so:
$(x+4)^2$

Answer:

The constant to add is $\boldsymbol{16}$.
The perfect square trinomial is $x^2 + 8x + 16$, which factors to $(x+4)^2$.