Factor 5x^2+24x-5

Problem

5*x2+24*x−5

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=5 b=24 and c=−5

2. Multiply the leading coefficient a and the constant term c to find the product a*c=5⋅(−5)=−25

3. Find two numbers that multiply to −25 and add to the middle coefficient b=24 These numbers are 25 and −1

4. Rewrite the middle term 24*x using the two numbers found: 25*x−x

5*x2+25*x−x−5

5. Factor by grouping the first two terms and the last two terms.

5*x*(x+5)−1*(x+5)

6. Factor out the common binomial factor (x+5)

(5*x−1)*(x+5)

Final Answer

5*x2+24*x−5=(5*x−1)*(x+5)

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