Factor 2x^2-x-15

Problem

2*x2−x−15

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=2 b=−1 and c=−15

2. Find two numbers that multiply to a⋅c=2⋅−15=−30 and add to b=−1

3. Determine the pair of numbers, which are −6 and 5 since (−6)⋅5=−30 and −6+5=−1

4. Rewrite the middle term −x using these two numbers as −6*x+5*x

2*x2−6*x+5*x−15

5. Factor by grouping by taking the greatest common factor out of the first two terms and the last two terms.

2*x*(x−3)+5*(x−3)

6. Factor out the common binomial (x−3)

(2*x+5)*(x−3)

Final Answer

2*x2−x−15=(2*x+5)*(x−3)

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