Factor 4n^2-15n-25

Problem

4*n2−15*n−25

Solution

1. Identify the coefficients of the quadratic expression in the form a*n2+b*n+c where a=4 b=−15 and c=−25

2. Calculate the product of a and c which is 4×−25=−100

3. Find two numbers that multiply to −100 and add to the middle coefficient b=−15 These numbers are −20 and 5

4. Rewrite the middle term −15*n using the two numbers found: −20*n+5*n

4*n2−20*n+5*n−25

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

4*n*(n−5)+5*(n−5)

6. Factor out the common binomial (n−5)

(4*n+5)*(n−5)

Final Answer

4*n2−15*n−25=(4*n+5)*(n−5)

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