Factor 4x^2-11x-3

Problem

4*x2−11*x−3

Solution

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

2. Multiply the leading coefficient a and the constant term c to find the product a*c=4×−3=−12

3. Find two numbers that multiply to −12 and add to the middle coefficient b=−11 These numbers are −12 and 1

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

5. Factor by grouping the first two terms and the last two terms: 4*x*(x−3)+1*(x−3)

6. Factor out the common binomial factor (x−3)

Final Answer

4*x2−11*x−3=(4*x+1)*(x−3)

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