Factor 3x^2-13x+4

Problem

3*x2−13*x+4

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=3 b=−13 and c=4

2. Find two numbers that multiply to a⋅c=3⋅4=12 and add to b=−13

3. Determine the factors of 12 that satisfy the condition, which are −12 and −1

4. Rewrite the middle term −13*x using these two numbers: 3*x2−12*x−x+4

5. Factor by grouping the first two terms and the last two terms: 3*x*(x−4)−1*(x−4)

6. Factor out the common binomial (x−4)

Final Answer

3*x2−13*x+4=(3*x−1)*(x−4)

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