Factor 3x^2+16x+5

Problem

3*x2+16*x+5

Solution

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

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

3. Determine the pair of numbers, which are 15 and 1

4. Rewrite the middle term 16*x using these two numbers as 15*x+x

3*x2+15*x+x+5

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

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

6. Factor out the common binomial (x+5)

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

Final Answer

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

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