Factor 7x^2-9x+2

Problem

7*x2−9*x+2

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=7 b=−9 and c=2

2. Find two numbers that multiply to a⋅c=14 and add to b=−9

3. Determine the two numbers, which are −7 and −2 since (−7)⋅(−2)=14 and −7+(−2)=−9

4. Rewrite the middle term −9*x using these two numbers as −7*x−2*x

7*x2−7*x−2*x+2

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

7*x*(x−1)−2*(x−1)

6. Factor out the common binomial (x−1)

(7*x−2)*(x−1)

Final Answer

7*x2−9*x+2=(7*x−2)*(x−1)

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