Question

Find the number to add to x^2 – 16x to make it a perfect square trinomial. Write that trinomial as the square of a binomial.

Answer 1

`\begin{gathered} \text{Given} \\ x^2-16x \end{gathered}`

Take half of the coefficient of the second term, and square it

`\begin{gathered} -16\cdot(1)/(2)=-8 \\ \\ (-8)^2=64 \end{gathered}`

Add the result to the given to make it a perfect square trinomial and factor it

`x^2-16x+64=(x-8)^2`