Factor 2x^2+5x+3

Problem

2*x2+5*x+3

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=2 b=5 and c=3

2. Find two numbers that multiply to a⋅c=6 and add to b=5 These numbers are 2 and 3

3. Rewrite the middle term 5*x using the two numbers found: 2*x+3*x

2*x2+2*x+3*x+3

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

2*x*(x+1)+3*(x+1)

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

(2*x+3)*(x+1)

Final Answer

2*x2+5*x+3=(2*x+3)*(x+1)

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