Factor 3x^2+5x-2

Problem

3*x2+5*x−2

Solution

1. Identify the coefficients of the quadratic expression 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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