Factor 4x^2-x-5

Problem

4*x2−x−5

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=4 b=−1 and c=−5

2. Find two numbers that multiply to a*c=4×(−5)=−20 and add to b=−1

3. Determine the pair of numbers, which are −5 and 4 since (−5)×4=−20 and −5+4=−1

4. Rewrite the middle term −x using these two numbers as −5*x+4*x

4*x2−5*x+4*x−5

5. Factor by grouping by taking the greatest common factor out of the first two terms and the last two terms.

x*(4*x−5)+1*(4*x−5)

6. Factor out the common binomial (4*x−5)

(4*x−5)*(x+1)

Final Answer

4*x2−x−5=(4*x−5)*(x+1)

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