Factor 2x^2+7x-15

Problem

2*x2+7*x−15

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=2 b=7 and c=−15

2. Find two numbers that multiply to a⋅c=2⋅(−15)=−30 and add to b=7

3. Determine the pair of numbers, which are 10 and −3 since 10⋅(−3)=−30 and 10 + (-3) = 7$.

4. Rewrite the middle term 7*x using the two numbers found: 2*x2+10*x−3*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+5)−3*(x+5)

6. Factor out the common binomial (x+5) to obtain the final factored form.

Final Answer

2*x2+7*x−15=(2*x−3)*(x+5)

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