divide and check

Question

Divide and Check. b^2 – 25 / b-7 =

Answer 1

First, we divide using long division.  Set the division. 

 

Since the is no b term in (b² - 25), we can write the polynomial as  b² + 0b - 25.

 

           ___________

(b - 7) | b² + 0b - 25

 

 

Perform the long division.

 

                      b   + 7

           ____________

(b - 7) | b² + 0b - 25

             b²  - 7b

            __________

                    7b - 25

                    7b - 49

                _________

                           24

 

 

The quotient is  (b + 7)

The remainder is 24

 

 

To check, we multiply the quotient by the term we divided by.  Then add the remainder.  If the result gives us back the original polynomial, it checks out.

       

 

(b + 7)(b - 7) + 24 =

 

b² - 7b + 7b - 49 + 24 =

 

b² - 25

 

This checks out.

 

 

 

 

Answer 2

1.  b*(b-7)=b^2-7*b, therefor b^2-25-(b^2-7*b) = 7*b - 25
2.  7*(b-7)=7*b-49, therfor 7*b-25-(7*b-49) = 24

 

so (b^2-25)/(b-7) = (b+7) + 24/(b-7)