Factor 4x^2-4x-15

Problem

4*x2−4*x−15

Solution

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

2. Calculate the product of a and c which is 4×−15=−60

3. Find two numbers that multiply to −60 and add to the middle coefficient b=−4 These numbers are −10 and 6

4. Rewrite the middle term −4*x using the two numbers found: 4*x2−10*x+6*x−15

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

6. Factor out the common binomial (2*x−5) to obtain the final factored form.

Final Answer

4*x2−4*x−15=(2*x+3)*(2*x−5)

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