Factor 3x^2-4x-15

Problem

3*x2−4*x−15

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=3 b=−4 and c=−15

2. Calculate the product of a and c which is 3×−15=−45

3. Find two numbers that multiply to −45 and add to the middle coefficient b=−4 These numbers are −9 and 5

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

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

6. Factor out the common binomial factor (x−3)

Final Answer

3*x2−4*x−15=(3*x+5)*(x−3)

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