Factor 4x^2+7x+3

Problem

4*x2+7*x+3

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=4 b=7 and c=3

2. Find two numbers that multiply to a⋅c=12 and add to b=7 These numbers are 3 and 4

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

4*x2+4*x+3*x+3

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

4*x*(x+1)+3*(x+1)

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

(4*x+3)*(x+1)

Final Answer

4*x2+7*x+3=(4*x+3)*(x+1)

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