Factor 3x^2-5x-2

Problem

3*x2−5*x−2

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=3 b=−5 and c=−2

2. Find two numbers that multiply to a⋅c=3⋅(−2)=−6 and add to b=−5

3. Determine the pair of numbers, which are −6 and 1 since (−6)⋅1=−6 and −6+1=−5

4. Rewrite the middle term −5*x using the two numbers found: 3*x2−6*x+x−2

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

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

Final Answer

3*x2−5*x−2=(3*x+1)*(x−2)

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