Factor 6x^2+x-2

Problem

6*x2+x−2

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=6 b=1 and c=−2

2. Find two numbers that multiply to a⋅c=6⋅−2=−12 and add to b=1

3. Determine that the two numbers are 4 and −3 since 4⋅−3=−12 and 4 + (-3) = 1$.

4. Rewrite the middle term x using these two numbers as 4*x−3*x

6*x2+4*x−3*x−2

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

2*x*(3*x+2)−1*(3*x+2)

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

(3*x+2)*(2*x−1)

Final Answer

6*x2+x−2=(3*x+2)*(2*x−1)

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