Question

How do you factor `3x^2 + 54x + 243`?

Answer 1

`3x^2+54x+243 = 3(x^2+18x+81) = 3(x+9)^2`

Explanation:

First separate the common scalar factor:

`3x^2+54x+243 = 3(x^2+18x+81)`

The remaining quadratic factor is recognisable as a perfect square trinomial in that it is of the form `a^2+2ab+b^2 = (a+b)^2` with `a=x` and `b=9`.

Hence:

`3(x^2+18x+81) = 3(x+9)^2`