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 the first two terms and the last two terms.

2*x*(x+3)−5*(x+3)

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

(2*x−5)*(x+3)

Final Answer

2*x2+x−15=(2*x−5)*(x+3)

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