Factor 7x^2-5x-2

Problem

7*x2−5*x−2

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=7 b=−5 and c=−2

2. Find two numbers that multiply to a⋅c=7⋅(−2)=−14 and add to b=−5

3. Determine the factors of −14 that satisfy the condition: −7 and 2 since (−7)⋅2=−14 and −7+2=−5

4. Rewrite the middle term −5*x using the two numbers found: 7*x2−7*x+2*x−2

5. Factor by grouping the first two terms and the last two terms: 7*x*(x−1)+2*(x−1)

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

Final Answer

7*x2−5*x−2=(7*x+2)*(x−1)

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