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

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Answer 1 · 2015-06-14T19:31:13

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

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:

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

How do you factor 3x^2 + 54x + 2433x^2 + 54x + 243?