Question

question
factor completely.
$3x^2 - 4x + 1$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(3\times1 = 3\) and add up to \(-4\). The numbers are \(-1\) and \(-3\) since \((-1)\times(-3)=3\) and \(-1 + (-3)=-4\).

Step2: Rewrite the middle term

Rewrite \(-4x\) as \(-3x - x\) in the quadratic expression:
\(3x^{2}-3x - x + 1\)

Step3: Group and factor

Group the first two terms and the last two terms:
\((3x^{2}-3x)+(-x + 1)\)
Factor out the greatest common factor from each group:
\(3x(x - 1)-1(x - 1)\)

Step4: Factor out the common binomial

Now, factor out the common binomial \((x - 1)\):
\((3x - 1)(x - 1)\)

Answer:

\((3x - 1)(x - 1)\)