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Question 1  Fill in the numbered blanks to complete the long division process.

 

Divide x2 + 2x – 30  by   x – 5

 

Step 1

               x

X – 5      x2            + 2x          - 30

              x2           - (1)                                                           Multiply x (x – 5)

                              (2)          -   (3)                                       

                                                                                              Subtract (x2 + 2x) – (x2 – 5x)  and bring down -30

 

What values should go in these numbered blanks?

 ________________

_________________

_________________

 

Step 2 (from Step 1 above)

               X         +  7

X – 5      x2            + 2x          - 30

              x2           - 5x                                                           

                             7x          -   30                                          

                                ‘(4)       -   (5)                        Multiply 7 (x – 5)

                                               (6)                           Subtract (7x – 30) – (7x – 35)

What values should go in these numbered blanks?

(4) ________________

(5)_________________

(6)_________________

        What is the remainder after step 2?  __________________________________

 

Problem 2….  Find all the zeros of the function:

 

X3 – 4x2 + x + 6 = 0

 

Use whatever methods you like, and explain how you found the zeros.

 Feb 6, 2020
 #1
avatar+109061 
+2

(1)    5x

(2)    7x

(3)   30

(4)   7x

(5)   35

(6)    5 

 

Remainder  = 5

 

Second one

 

x^3  - 4x^2  + x  + 6   =  0

 

Note  that.....using  the Rational Zeros  Theorem that  2  is a root    (a zero)

 

So   using synthetic division to find the remaing polynomial  we have that

 

 

2  [  1     -  4       1        6  ]

                2       -4       -6

      ___________________

       1     -2       -3        0

 

The remaining polynomial  is     x^2  - 2x  - 3

 

Set to 0   and we have that

 

x^2 - 2x  - 3  =  0      factor

 

(x - 3) ( x + 1)  = 0

 

Set each factor to 0 and solve for x and the other two zeros are   3   and -1

 

So....the zeros  are

 

-1 , 2  and  3

 

 

 

 

cool cool cool

 Feb 6, 2020

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