Factor 5x^2+13x-6

Problem

5*x2+13*x−6

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=5 b=13 and c=−6

2. Find two numbers that multiply to a*c=5⋅(−6)=−30 and add to b=13

3. Determine that the two numbers are 15 and −2 since 15⋅(−2)=−30 and 15 + (-2) = 13$.

4. Rewrite the middle term 13*x using these two numbers.

5*x2+15*x−2*x−6

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

5*x*(x+3)−2*(x+3)

6. Factor out the common binomial (x+3)

(5*x−2)*(x+3)

Final Answer

5*x2+13*x−6=(5*x−2)*(x+3)

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