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1. Cristoble used synthetic division to divide the polynomial f(x) by x + 3, as shown on the table.

What is the value of f(−3) ?

 

2.

Which binomial expressions are factors of 4x^3+9x^2−x−6?    
Select EACH correct answer.

 

A) x−1

B) x + 2

C) x + 1

D) x−2

 

3.Three is a zero of the equation x^3−4x^2−3x+18=0.

Which factored form is equivalent to the equation?

A) (x−2)(x−3)(x+3)=0

B) (x−2)(x−3)^2=0

C) (x+2)(x−3)^2=0

D) (x+2)(x−√3)(x+√3)=0

 

4.

Which values are possible rational roots of 4x^3+9x^2−x+10=0 according to the rational root theorem?

Select EACH correct answer.

 

A) ±52

B) ±25

C) ±12

D) ±2

oscar.a1551  Oct 25, 2018
 #1
avatar+90995 
+2

1) f(-3)   = 36

 

2)  4x^3+9x^2−x−6

 

-1 is  a root because    4(-1)^3  + 9(-1)^2 - (-1)  - 6  =     -4   + 9 + 1   - 6 =  -5 + 5  = 0

 

So  (x + 1)  is one factor

 

Performing some synthetic division  to find the remaining polynomial  we have

 

-1  [  4   9     - 1   - 6  ]

            -4      -5     6

     ________________

       4    5      -6

 

So....the remaining polynomial is    4x^2  + 5x  - 6

 

Factoring this we have

 

( 4x - 3) ( x + 2)

 

So...the factors are  ( x + 1) (x + 2) (4x - 3)

 

 

3) Since we know that 3 is a zero...we can perform some synthetic division to find the other factors

 

  3   [ 1  - 4  - 3   18  ]

               3   -3   -18

      _______________

         1   -1   -6

 

The remaining polynomial is    x^2  - x   - 6    which factors as    (x - 3) ( x + 2)

 

So...the factorization is

 

(x - 3) ( x - 3) ( x + 2)   =  (x + 2)  (x - 3)^2

 

 

4) Possible  rational roots   =  all the factors of 10  =  1, 2, 5, 10   over all the  factors of 4  =  1, 2, 4

 

So...   ±5/2  , ±1/2  and ± 2

 

 

 

 

cool cool cool

CPhill  Oct 25, 2018

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