Factor 3x^2-11x-4

Problem

3*x2−11*x−4

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=3 b=−11 and c=−4

2. Find two numbers that multiply to a⋅c=3⋅(−4)=−12 and add to b=−11

3. Determine the numbers to be −12 and 1 since (−12)⋅1=−12 and −12+1=−11

4. Rewrite the middle term −11*x using these two numbers: 3*x2−12*x+x−4

5. Factor by grouping by taking the greatest common factor out of the first two terms and the last two terms: 3*x*(x−4)+1*(x−4)

6. Factor out the common binomial (x−4) to obtain the final factored form.

Final Answer

3*x2−11*x−4=(3*x+1)*(x−4)

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