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# Algebra

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1. (a)  Given the following equation,    x^4-x^3-3x-2 use synthetic division to test the following 3 pts and show if they are a root or not.   Must show synthetic division for all 3 of the following test pts.   Test these 3 possible root pts also called possible zeros using synthetic division.   (x,y) =  (-3, 0) ;   ( -1, 0)   ;   (2, 0).

(Score for Question 2: ___ of 5 points)

1.  Using the rational root theorem, list the possible zeros:

here is an example: 6x^3+8x^2-7x-3=0

q                    p

Factors of p: +-1, +- 3

factors of q: +-1, +-2, +-3, +-6

Possible zeros +-p/q

+-1, +-1/2, +-1/3, +-1/6, +-3, +-3/2

Using p/q list all the possible zeros of the following equation:4x^2 – 6x -11 = 0.

List factors of p:

List factors of q:

List possible zeros:+/- p/q

May also use a punnet square to show 12 possible answers as shown in class (plus and minus each case makes 2 of the 12)

(Score for Question 3: ___ of 5 points)

1. Simplify the expression   (x^4+4x^3-5x-20)÷(x+4)   using synthetic division. Show your work just an answer without showing the synthetic division will get a zero grade.   After doing the synthetic division, which gives you just coefficients.  Convert the coefficient quotient answer, into a polynomial with variable x and the correct exponent powers in it.   Convert your coefficient answer into a polynomial.

Hint:remember to fill in any missing degree terms in your dividend with coefficients that are zero to represent missing place holders.Hint2 :Your final remainder is a zero.If you do not get a zero as a remainder, you are doing something wrong.

Apr 12, 2021

#1
+118626
+1

1)

- 3  [  1    -  1      0       -  3     - 2  ]

-  3     12      -36    117

_________________________

1       -4     12      -39     115                    not a root

-1  [  1       - 1       0     - 3       -2  ]

-1        2    - 2        5

________________________

1     -2        2      -5        3                 not a root

2  [  1   - 1    0       -  3      -  2  ]

2     2         4           2

___________________________

1     1     2          1          0                   is a  root

Apr 12, 2021
#2
+118626
+1

2)    4x^2  -  6x  -  11

p  = ± [ 1 , 11]

q  =  ± [ 1 , 2 , 4 ]

p/q  =  ± [ 1 , 1/2 1/4 , 11 , 11/2 , 11/4 ]

Apr 12, 2021
#3
+118626
+1

3)     (x^4  + 4x^3  - 5x  - 20)  / (x + 4)

We   are  testing to see if  - 4  is a root....so....

-4  [  1     4        0         -  5        -20     ]

-4        0           0          20

_____________________________

1     0         0        -5             0

-4 is a root

The remaining polynomial  is      x^3   -   5

Apr 12, 2021