Factor 6w^2-7w+1

Problem

6*w2−7*w+1

Solution

1. Identify the coefficients of the quadratic expression a*w2+b*w+c where a=6 b=−7 and c=1

2. Find two numbers that multiply to a⋅c=6 and add to b=−7

3. Determine the numbers, which are −6 and −1 since (−6)⋅(−1)=6 and −6+(−1)=−7

4. Rewrite the middle term −7*w using these two numbers as 6*w2−6*w−w+1

5. Factor by grouping by taking the greatest common factor out of the first two terms and the last two terms: 6*w*(w−1)−1*(w−1)

6. Factor out the common binomial (w−1) to obtain the final factored form.

Final Answer

6*w2−7*w+1=(6*w−1)*(w−1)

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