Factor 4x^2+16x+15

Problem

4*x2+16*x+15

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=4 b=16 and c=15

2. Find two numbers that multiply to a⋅c=4⋅15=60 and add to b=16

3. Determine the factors of 60 that sum to 16 which are 6 and 10

4. Rewrite the middle term 16*x using these two numbers as 6*x+10*x

4*x2+6*x+10*x+15

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

2*x*(2*x+3)+5*(2*x+3)

6. Factor out the common binomial (2*x+3)

(2*x+3)*(2*x+5)

Final Answer

4*x2+16*x+15=(2*x+3)*(2*x+5)

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