Factor 5x^2+3x-2

Problem

5*x2+3*x−2

Solution

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

2. Find two numbers that multiply to a⋅c=5⋅(−2)=−10 and add to b=3

3. Determine the factors of −10 that satisfy the condition: 5 and −2 work because 5⋅(−2)=−10 and 5 + (-2) = 3$.

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

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

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

Final Answer

5*x2+3*x−2=(5*x−2)*(x+1)

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