Factor 4x^2+9x+5

Problem

4*x2+9*x+5

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=4 b=9 and c=5

2. Find two numbers that multiply to a*c=4⋅5=20 and add to b=9 These numbers are 4 and 5

3. Rewrite the middle term 9*x using the two numbers found: 4*x+5*x

4*x2+4*x+5*x+5

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)+5*(x+1)

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

(4*x+5)*(x+1)

Final Answer

4*x2+9*x+5=(4*x+5)*(x+1)

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