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# I need help with a few questions...

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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

Oct 25, 2018

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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   Oct 25, 2018