Factor 3x^2+13x-10

Problem

3*x2+13*x−10

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=3 b=13 and c=−10

2. Find two numbers that multiply to a⋅c=3⋅(−10)=−30 and add to b=13

3. Determine the pair of numbers, which are 15 and −2 since 15⋅(−2)=−30 and 15 + (-2) = 13$.

4. Rewrite the middle term 13*x using the two numbers found: 15*x−2*x

3*x2+15*x−2*x−10

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

3*x*(x+5)−2*(x+5)

6. Factor out the common binomial (x+5)

(3*x−2)*(x+5)

Final Answer

3*x2+13*x−10=(3*x−2)*(x+5)

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