Factor 3x^2-14x+15

Problem

3*x2−14*x+15

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=3 b=−14 and c=15

2. Multiply the leading coefficient a and the constant term c to find the product a*c=3⋅15=45

3. Find two numbers that multiply to 45 and add to the middle coefficient b=−14 These numbers are −9 and −5

4. Rewrite the middle term −14*x using the two numbers found: 3*x2−9*x−5*x+15

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

6. Factor out the common binomial (x−3) to obtain the final factored form.

Final Answer

3*x2−14*x+15=(3*x−5)*(x−3)

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