Factor 2x^2+9x+10

Problem

2*x2+9*x+10

Solution

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

2. Find two numbers that multiply to a⋅c=20 and add to b=9

3. Determine that the two numbers are 4 and 5 because 4⋅5=20 and 4 + 5 = 9$.

4. Rewrite the middle term 9*x using these two numbers.

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

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

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

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

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

Final Answer

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

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