Question

factor out a monomial before factoring completely. 1) $3x^3 - 15x^2 + 18x$

Explanation:

Step1: Factor out the GCF monomial

The greatest common factor (GCF) of \(3x^{3}\), \(-15x^{2}\), and \(18x\) is \(3x\). Factor it out:
\(3x^{3}-15x^{2}+18x = 3x(x^{2}-5x + 6)\)

Step2: Factor the quadratic trinomial

Factor \(x^{2}-5x + 6\). We need two numbers that multiply to \(6\) and add to \(-5\). Those numbers are \(-2\) and \(-3\):
\(x^{2}-5x + 6=(x - 2)(x - 3)\)

Step3: Combine the factors

Substitute the factored quadratic back into the expression:
\(3x(x^{2}-5x + 6)=3x(x - 2)(x - 3)\)

Answer:

\(3x(x - 2)(x - 3)\)