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. Calculate the product of a and c which is 6⋅(−1)=−6

3. Find two numbers that multiply to −6 and add to the middle coefficient b=−1 These numbers are −3 and 2

4. Rewrite the middle term −x using the two numbers found: −3*x+2*x

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 factor (2*x−1)

(3*x+1)*(2*x−1)

Final Answer

6*x2−x−1=(3*x+1)*(2*x−1)

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