Factor 2x^2+3x-9

Problem

2*x2+3*x−9

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=2 b=3 and c=−9

2. Find two numbers that multiply to a⋅c=2⋅−9=−18 and add to b=3

3. Determine that the two numbers are 6 and −3 since 6⋅−3=−18 and 6 + (-3) = 3$.

4. Rewrite the middle term 3*x using these two numbers: 2*x2+6*x−3*x−9

5. Factor by grouping the first two terms and the last two terms: 2*x*(x+3)−3*(x+3)

6. Factor out the common binomial factor (x+3)

Final Answer

2*x2+3*x−9=(2*x−3)*(x+3)

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