Factor 6x^2+x-1

Problem

6*x2+x−1

Solution

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

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

3. Determine that the two numbers are 3 and −2 because 3⋅(−2)=−6 and 3 + (-2) = 1$.

4. Rewrite the middle term x using these two numbers: 6*x2+3*x−2*x−1

5. Factor by grouping the first two terms and the last two terms: 3*x*(2*x+1)−1*(2*x+1)

6. Factor out the common binomial (2*x+1) to obtain the final factored form.

Final Answer

6*x2+x−1=(3*x−1)*(2*x+1)

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