Factor 5x^2+26x+5

Problem

5*x2+26*x+5

Solution

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

2. Find two numbers that multiply to a⋅c=25 and add to b=26

3. Determine that the two numbers are 25 and 1 since 25⋅1=25 and 25 + 1 = 26$.

4. Rewrite the middle term 26*x using these two numbers as 25*x+x

5*x2+25*x+x+5

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)+1*(x+5)

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

(5*x+1)*(x+5)

Final Answer

5*x2+26*x+5=(5*x+1)*(x+5)

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