Factor 5x^2+26x+24

Problem

5*x2+26*x+24

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=5 b=26 and c=24

2. Calculate the product a*c by multiplying 5 and 24

5⋅24=120

3. Find two numbers that multiply to 120 and add up to the middle coefficient b=26

20⋅6=120

20+6=26

4. Rewrite the middle term 26*x using the two numbers found in the previous step.

5*x2+20*x+6*x+24

5. Factor by grouping by taking the greatest common factor out of the first two terms and the last two terms.

5*x*(x+4)+6*(x+4)

6. Factor out the common binomial factor (x+4)

(5*x+6)*(x+4)

Final Answer

5*x2+26*x+24=(5*x+6)*(x+4)

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