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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