Question

Which of the following is a factor of 3x3 + 18x2 + 27x

Answer 1

So firstly, we have to factor out the GCF, or greatest common factor, of these terms. To find the GCF, list the factors of each term and the greatest one they share is their GCF. In this case, the GCF is 3x:

$3x(x^2+6x+9)$

Next, what's inside the parentheses is considered a perfect square. Using this format of $(a+b)^2=a^2+2ab+b^2$ , we can factor it as such:

$x^2+6x+9=(x+3)^2\\3x(x+3)^2\\3x(x+3)(x+3)$

The factors of this expression are 3x, x + 3, and x + 3.