Factor 2x^2+5x+2

Problem

2*x2+5*x+2

Solution

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

2. Find two numbers that multiply to a⋅c=4 and add to b=5 These numbers are 4 and 1

3. Rewrite the middle term 5*x using the two numbers found: 4*x+x

2*x2+4*x+x+2

4. Group the terms into two pairs.

(2*x2+4*x)+(x+2)

5. Factor out the greatest common factor from each pair.

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

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

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

Final Answer

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

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