Factor 2x^2+9x+4

Problem

2*x2+9*x+4

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=2 b=9 and c=4

2. Find two numbers that multiply to a⋅c=2⋅4=8 and add to b=9 These numbers are 8 and 1

3. Rewrite the middle term 9*x using the two numbers found: 8*x+1*x

2*x2+8*x+x+4

4. Factor by grouping the first two terms and the last two terms.

(2*x2+8*x)+(x+4)

5. Factor out the greatest common factor from each group.

2*x*(x+4)+1*(x+4)

6. Factor out the common binomial factor (x+4)

(2*x+1)*(x+4)

Final Answer

2*x2+9*x+4=(2*x+1)*(x+4)

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