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

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Answer 1 · 2018-06-12T12:10:42

#(x+7)^2#

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

Answer 2 · 2018-06-12T14:01:51

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

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#