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# 1. Kristina used synthetic division to divide the polynomial f(x) by x−2, as shown on the table.

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1. Kristina used synthetic division to divide the polynomial f(x) by x−2, as shown on the table.

What is the value of f(2)?

A).-14     B).-1   C).-2   D).-1 2. Which binomial expressions are factors of 2x3+5x2−x−6?

Select each correct answer.

X+1

X-2

X-1

X+2

3. Three is a zero of the equation x3−4x2−3x+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√)(x+3√)=0

D). (x−2)(x−3)2=0

Oct 23, 2017

#1
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The answer to the  first one sould be  -11

2x^3 +5x^2−x−6

Write 5x^2  as  4x^2 + x^2......and we have.....

2x^3 + 4x^2 + x^2 - x - 6

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

(x + 2) [ 2x^2 + x - 3]

(x + 2) (2x +3) (x - 1)

x^3−4x^2−3x+18 = 0

Using some synthetic division, we have

3  [   1   - 4      -3      18  ]

3      -3     -18

_______________

1    -1      -6       0

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

So ....   the factored form is  (x - 3) ( x - 3) ( x + 2)  = ( x + 2) ( x - 3)^2 = 0   Oct 23, 2017