Question

Determine whether `x^2+14x+49` is a perfect square trinomial, if so, how do you factor it.?

Answer 1

`(x+7)^2`

Explanation:

And tis is `(x+7)*(x+7)`

Answer 2

`x^2 +14x+49 = (x+7)(x+7) = (x+7)^2`

Explanation:

There are a few things to look for in a perfect square trinomial.

• the first term must be a perfect square
• the third term must be a perfect square ( and a positive term)
• the middle term must be made up of twice the product of the square roots of the first term and third term.

In this case: `color(blue)(x^2)+14x" " color(red)( +49)`

`color(blue)(x^2)` is a perfect square and `color(blue)(sqrt(x^2) =x)`
`color(red)(49)` is a perfect square and `color(red)(sqrt(49) =7)`

The middle term consists of `2 xxcolor(blue)(x)xxcolor(red)(7) =14x`

`x^2 +14x+49 = (x+7)(x+7) = (x+7)^2`