Factor 3x^2-x-10

Problem

3*x2−x−10

Solution

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

2. Find two numbers that multiply to a⋅c=3⋅(−10)=−30 and add to b=−1

3. Determine the pair of numbers, which are −6 and 5 since (−6)⋅5=−30 and −6+5=−1

4. Rewrite the middle term −x using these two numbers: 3*x2−6*x+5*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−2)+5*(x−2)

6. Factor out the common binomial (x−2) to obtain the final factored form.

Final Answer

3*x2−x−10=(3*x+5)*(x−2)

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