Factor 2x^2+7x+5

Problem

2*x2+7*x+5

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=2 b=7 and c=5

2. Find two numbers that multiply to a⋅c=10 and add to b=7

3. Determine that the two numbers are 2 and 5 since 2⋅5=10 and 2 + 5 = 7$.

4. Rewrite the middle term 7*x using these two numbers as 2*x+5*x

2*x2+2*x+5*x+5

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

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

6. Factor out the common binomial (x+1)

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

Final Answer

2*x2+7*x+5=(2*x+5)*(x+1)

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