Question

completely factor each expression: c. $3x^2 - 15x + 18$

Explanation:

Step1: Factor out the GCF

The greatest common factor (GCF) of \(3x^2\), \(-15x\), and \(18\) is \(3\). So we factor out \(3\) from the expression:
\(3x^2 - 15x + 18 = 3(x^2 - 5x + 6)\)

Step2: Factor the quadratic trinomial

Now we need to factor the quadratic \(x^2 - 5x + 6\). We look for two numbers that multiply to \(6\) (the constant term) and add up to \(-5\) (the coefficient of the \(x\)-term). The numbers \(-2\) and \(-3\) work because \((-2) \times (-3) = 6\) and \((-2) + (-3) = -5\). So we can factor \(x^2 - 5x + 6\) as \((x - 2)(x - 3)\).

Putting it all together, the completely factored form of the original expression is:
\(3(x - 2)(x - 3)\)

Answer:

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