Factor 5x^2-22x-15

Problem

5*x2−22*x−15

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=5 b=−22 and c=−15

2. Find two numbers that multiply to a⋅c=5⋅(−15)=−75 and add to b=−22

3. Determine the pair of numbers, which are −25 and 3 since (−25)⋅3=−75 and −25+3=−22

4. Rewrite the middle term −22*x using these two numbers: 5*x2−25*x+3*x−15

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

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

Final Answer

5*x2−22*x−15=(5*x+3)*(x−5)

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