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

`((7)/(2))^2=(49)/(4)`

so the expresion is

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

and the factor

`(w+(7)/(2))^2`

An example

`w^2+(8)/(5)w+\cdots_{}`

the third term is

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

so the percet-square is

`w^2+(8)/(5)w+(16)/(25)`