Factor 5x^2+7x+2

Problem

5*x2+7*x+2

Solution

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

2. Find two numbers that multiply to a⋅c=10 and add to b=7 These numbers are 5 and 2

3. Rewrite the middle term 7*x using the two numbers found in the previous step.

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

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

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

5. Factor out the common binomial factor (x+1)

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

Final Answer

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

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