Factor 2x^2+7x+3

Problem

2*x2+7*x+3

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=2 b=7 and c=3

2. Find two numbers that multiply to a⋅c=2⋅3=6 and add to b=7

3. Determine the pair of numbers, which are 6 and 1 since 6⋅1=6 and 6 + 1 = 7$.

4. Rewrite the middle term 7*x using the two numbers found: 2*x2+6*x+1*x+3

5. Factor by grouping the first two terms and the last two terms: 2*x*(x+3)+1*(x+3)

6. Factor out the common binomial factor (x+3)

Final Answer

2*x2+7*x+3=(2*x+1)*(x+3)

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