How do you know if # x^2 + 8x + 16# is a perfect square trinomial and how do you factor it?

1 Answer
May 2, 2018

Answer:

It is a perfect square. Explanation below.

Explanation:

Perfect squares are of the form #(a + b)^2 = a^2 + 2ab + b^2#. In polynomials of x, the a-term is always x.(#(x+c)^2 = x^2 + 2cx + c^2#)

#x^2 + 8x + 16# is the given trinomial. Notice that the first term and the constant are both perfect squares: #x^2# is the square of x and 16 is the square of 4.

So we find that the first and last terms correspond to our expansion. Now we must check if the middle term, #8x# is of the form #2cx#.

The middle term is twice the constant times x, so it is #2xx4xxx = 8x#.

Okay, we found out that the trinomial is of the form #(x+c)^2#, where #x = x and c = 4#.

Let us rewrite it as #x^2 + 8x + 16 = (x+4)^2#. Now we can say it is a perfect square, as it is the square of #(x+4)#.