Factor 2x^2+13x-24

Problem

2*x2+13*x−24

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=2 b=13 and c=−24

2. Calculate the product of a and c which is 2×−24=−48

3. Find two numbers that multiply to −48 and add to the middle coefficient b=13 These numbers are 16 and −3

4. Rewrite the middle term 13*x using the two numbers found: 16*x−3*x

2*x2+16*x−3*x−24

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

2*x*(x+8)−3*(x+8)

6. Factor out the common binomial (x+8)

(2*x−3)*(x+8)

Final Answer

2*x2+13*x−24=(2*x−3)*(x+8)

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