Factor 20x^2+22x-12

Problem

20*x2+22*x−12

Solution

1. Factor out the greatest common factor (GCF) from all three terms, which is 2

2*(10*x2+11*x−6)

2. Identify the coefficients a b and c from the quadratic expression inside the parentheses 10*x2+11*x−6

a=10

b=11

c=−6

3. Find two numbers that multiply to a⋅c=−60 and add to b=11

15⋅−4=−60

15+(−4)=11

4. Rewrite the middle term 11*x using the two numbers found in the previous step.

2*(10*x2+15*x−4*x−6)

5. Factor by grouping the terms inside the parentheses.

2*([[*10*x2+15*x]]+[[−4*x−6*]])

6. Extract the GCF from each group.

2*(5*x*(2*x+3)−2*(2*x+3))

7. Factor out the common binomial (2*x+3)

2*(2*x+3)*(5*x−2)

Final Answer

20*x2+22*x−12=2*(2*x+3)*(5*x−2)

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