Factor 2x^2-7x-4

Problem

2*x2−7*x−4

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=2 b=−7 and c=−4

2. Calculate the product of a and c which is 2×−4=−8

3. Find two numbers that multiply to −8 and add to the middle coefficient b=−7 These numbers are −8 and 1

4. Rewrite the middle term −7*x using the two numbers found: 2*x2−8*x+1*x−4

5. Factor by grouping the first two terms and the last two terms: 2*x*(x−4)+1*(x−4)

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

Final Answer

2*x2−7*x−4=(2*x+1)*(x−4)

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