Factor 5x^2+9x-2

Problem

5*x2+9*x−2

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=5 b=9 and c=−2

2. Find two numbers that multiply to a⋅c=5⋅(−2)=−10 and add to b=9

3. Determine the pair of numbers, which are 10 and −1

4. Rewrite the middle term 9*x using these two numbers as 10*x−x

5*x2+10*x−x−2

5. Group the terms into two pairs.

(5*x2+10*x)+(−x−2)

6. Factor out the greatest common factor from each pair.

5*x*(x+2)−1*(x+2)

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

(5*x−1)*(x+2)

Final Answer

5*x2+9*x−2=(5*x−1)*(x+2)

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