Question

Factor the following trinomial. 16x2 + 8x + 1

Answer 1

Factoring a trinomial

In the following trinomial

`16x^2+8x+1`

We find the first and second terms can be written

`\begin{gathered} 16x^2=(4x)^2 \\ 8x=2(4x) \end{gathered}`

Since the perfect square trinomial is given by the equation

`(A+B)^2=A^2+2AB+B`

If we replace A = 4x and B = 1, then, the last equation is

`\begin{gathered} A^2+2AB+B=(4x)^2+2(4x)\cdot1+1 \\ =16x^2+8x+1 \end{gathered}`

Then, we can factor the given trinomial using the perfect square trinomial equation:

`16x^2+8x+1=(4x+1)^2`