Factor 5x^2+11x+2

Problem

5*x2+11*x+2

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=5 b=11 and c=2

2. Find two numbers that multiply to a⋅c=5⋅2=10 and add to b=11

3. Determine the pair of numbers, which are 10 and 1 since 10⋅1=10 and 10 + 1 = 11$.

4. Rewrite the middle term 11*x using these two numbers as 10*x+x

5*x2+10*x+x+2

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

5*x*(x+2)+1*(x+2)

6. Factor out the common binomial (x+2)

(5*x+1)*(x+2)

Final Answer

5*x2+11*x+2=(5*x+1)*(x+2)

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