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 the pair of numbers, which are −6 and 3 since (−6)⋅3=−18 and −6+3=−3

4. Rewrite the middle term −3*x using the two numbers found: 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 (x−3) to obtain the final factored form.

Final Answer

2*x2−3*x−9=(2*x+3)*(x−3)

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