Factor 10x^2+9x+2

Problem

10*x2+9*x+2

Solution

1. Identify the coefficients a b and c from the quadratic expression a*x2+b*x+c where a=10 b=9 and c=2

2. Calculate the product a*c which is 10⋅2=20

3. Find two numbers that multiply to 20 and add to b=9 These numbers are 4 and 5

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

10*x2+4*x+5*x+2

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

2*x*(5*x+2)+1*(5*x+2)

6. Factor out the common binomial (5*x+2)

(2*x+1)*(5*x+2)

Final Answer

10*x2+9*x+2=(2*x+1)*(5*x+2)

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