Question

factor out the greatest common factor. 3x³ + 7x² + 27x ? (3x² + 7x + 27)

Explanation:

Step1: Identify the GCF of coefficients and variables

For the terms \(3x^3\), \(7x^2\), and \(27x\):

• The coefficients are 3, 7, 27. The GCF of 3, 7, 27 is 1? Wait, no, wait for the variable part. The variable part: \(x^3\), \(x^2\), \(x\). The lowest power of \(x\) is \(x^1 = x\). Wait, but let's check each term:

\(3x^3 = x\times3x^2\)
\(7x^2 = x\times7x\)
\(27x = x\times27\)
So the greatest common factor (GCF) of the three terms is \(x\).

Step2: Factor out the GCF

We factor out \(x\) from \(3x^3 + 7x^2 + 27x\):
\(3x^3 + 7x^2 + 27x = x(3x^2 + 7x + 27)\)

Answer:

\(x\)