Factor 3n^2-8n+4

Problem

3*n2−8*n+4

Solution

1. Identify the coefficients of the quadratic expression a*n2+b*n+c where a=3 b=−8 and c=4

2. Find two numbers that multiply to a⋅c=3⋅4=12 and add to b=−8

3. Determine that the two numbers are −6 and −2 since (−6)*(−2)=12 and −6+(−2)=−8

4. Rewrite the middle term −8*n using these two numbers: 3*n2−6*n−2*n+4

5. Factor by grouping by taking the greatest common factor out of the first two terms and the last two terms: 3*n*(n−2)−2*(n−2)

6. Factor out the common binomial (n−2) to obtain the final factored form.

Final Answer

3*n2−8*n+4=(3*n−2)*(n−2)

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