Factor 2x^2+13x+20

Problem

2*x2+13*x+20

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=2 b=13 and c=20

2. Calculate the product of a and c which is 2×20=40

3. Find two numbers that multiply to 40 and add up to the middle coefficient b=13 These numbers are 5 and 8

4. Rewrite the middle term 13*x using the two numbers found: 5*x+8*x

2*x2+8*x+5*x+20

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

2*x*(x+4)+5*(x+4)

6. Extract the common binomial factor (x+4)

(2*x+5)*(x+4)

Final Answer

2*x2+13*x+20=(2*x+5)*(x+4)

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