Factor 16b^2+60b-100

Problem

16*b2+60*b−100

Solution

1. Factor out the greatest common factor (GCF) from all three terms, which is 4

4*(4*b2+15*b−25)

2. Identify the coefficients of the quadratic expression inside the parentheses, 4*b2+15*b−25 where a=4 b=15 and c=−25

3. Find two numbers that multiply to a⋅c=4⋅(−25)=−100 and add to b=15 These numbers are 20 and −5

4. Rewrite the middle term 15*b using the two numbers found in the previous step.

4*(4*b2+20*b−5*b−25)

5. Factor by grouping the terms inside the parentheses.

4*((4*b2+20*b)+(−5*b−25))

6. Factor out the GCF from each group.

4*(4*b*(b+5)−5*(b+5))

7. Factor out the common binomial (b+5)

4*(4*b−5)*(b+5)

Final Answer

16*b2+60*b−100=4*(4*b−5)*(b+5)

Want more problems? Check here!