Factor 2x^2-3x-5

Problem

2*x2−3*x−5

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=2 b=−3 and c=−5

2. Find two numbers that multiply to a⋅c=2⋅(−5)=−10 and add to b=−3

3. Determine the pair of numbers, which are −5 and 2 since (−5)⋅2=−10 and −5+2=−3

4. Rewrite the middle term −3*x using the two numbers found: 2*x2+2*x−5*x−5

5. Factor by grouping the first two terms and the last two terms: 2*x*(x+1)−5*(x+1)

6. Factor out the common binomial factor (x+1)

Final Answer

2*x2−3*x−5=(2*x−5)*(x+1)

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