Factor 2n^2+3n-9

Problem

2*n2+3*n−9

Solution

1. Identify the coefficients of the quadratic expression in the form a*n2+b*n+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 the pair of numbers, which are 6 and −3 since 6⋅−3=−18 and 6 + (-3) = 3$.

4. Rewrite the middle term 3*n using the pair of numbers found: 2*n2+6*n−3*n−9

5. Factor by grouping by taking the greatest common factor out of the first two terms and the last two terms: 2*n*(n+3)−3*(n+3)

6. Factor out the common binomial (n+3) to obtain the final factored form.

Final Answer

2*n2+3*n−9=(2*n−3)*(n+3)

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