Question

First find the term that should be added so that the expression is a perfect-square trinomial. w² + 7w + ___Then factor the trinomial.(___)²

Answer 1

to do a perfect-square trinomial the third term must be the square of the half of the second term

the sencond term is 7,so

$(\frac{7}{2})^2=\frac{49}{4}$

so the expresion is

$w^2+7w+\frac{49}{4}$

and the factor

$(w+\frac{7}{2})^2$

An example

$w^2+\frac{8}{5}w+\cdots_{}$

the third term is

$\begin{gathered} (\frac{\frac{8}{5}}{2})^2 \\ \\ (\frac{4}{5})^2 \\ \\ =\frac{16}{25} \end{gathered}$

so the percet-square is

$w^2+\frac{8}{5}w+\frac{16}{25}$