Factor 5x^2+16x+3

Problem

5*x2+16*x+3

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=5 b=16 and c=3

2. Find two numbers that multiply to a⋅c=5⋅3=15 and add to b=16

3. Determine the pair of numbers, which are 15 and 1 since 15⋅1=15 and 15 + 1 = 16$.

4. Rewrite the middle term 16*x using the two numbers found: 15*x+x

5*x2+15*x+x+3

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

5*x*(x+3)+1*(x+3)

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

(5*x+1)*(x+3)

Final Answer

5*x2+16*x+3=(5*x+1)*(x+3)

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