Factor 4x^2+12x+5

Problem

4*x2+12*x+5

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=4 b=12 and c=5

2. Find two numbers that multiply to a⋅c=20 and add to b=12 These numbers are 10 and 2

3. Rewrite the middle term 12*x using the two numbers found: 10*x+2*x

4*x2+10*x+2*x+5

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

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

5. Factor out the common binomial factor (2*x+5)

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

Final Answer

4*x2+12*x+5=(2*x+5)*(2*x+1)

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