Factor 3x^2-13x-10

Problem

3*x2−13*x−10

Solution

1. Identify the coefficients of the quadratic expression in the form 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: 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) to obtain the final factored form.

Final Answer

3*x2−13*x−10=(3*x+2)*(x−5)

Want more problems? Check here!