Factor 3x^2-14x+8

Problem

3*x2−14*x+8

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=3 b=−14 and c=8

2. Calculate the product a*c which is 3⋅8=24

3. Find two numbers that multiply to 24 and add to the middle coefficient b=−14 These numbers are −12 and −2

4. Rewrite the middle term −14*x using the two numbers found: 3*x2−12*x−2*x+8

5. Factor by grouping by taking the greatest common factor out of the first two terms and the last two terms: 3*x*(x−4)−2*(x−4)

6. Factor out the common binomial (x−4) to obtain the final factored form.

Final Answer

3*x2−14*x+8=(3*x−2)*(x−4)

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