Factor 5x^2+28x+15

Problem

5*x2+28*x+15

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=5 b=28 and c=15

2. Calculate the product a*c which is 5×15=75

3. Find two numbers that multiply to 75 and add up to the middle coefficient b=28 These numbers are 25 and 3

4. Rewrite the middle term 28*x using the two numbers found: 25*x+3*x

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)

(5*x+3)*(x+5)

Final Answer

5*x2+28*x+15=(5*x+3)*(x+5)

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