Factor 2x^2+3x-20

Problem

2*x2+3*x−20

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=2 b=3 and c=−20

2. Calculate the product a*c which is 2×−20=−40

3. Find two numbers that multiply to −40 and add to the middle coefficient b=3 These numbers are 8 and −5

4. Rewrite the middle term 3*x using the two numbers found: 8*x−5*x

2*x2+8*x−5*x−20

5. Factor by grouping the first two terms and the last two terms.

2*x*(x+4)−5*(x+4)

6. Factor out the common binomial factor (x+4)

(2*x−5)*(x+4)

Final Answer

2*x2+3*x−20=(2*x−5)*(x+4)

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