Use synthetic division to find quotient and remainder: (2x^3-6x^2+4x-2) divided  by (2x-1)

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embizze's profile pic

embizze | High School Teacher | (Level 1) Educator Emeritus

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Use synthetic division to divide `2x^3-6x^2+4x-2` by `(2x-1)` .

The divisor will be 1/2 (If 2x-1 is a factor then x=1/2 is a root).Thus

` `1/2 | 2   -6     4     -2
1   -5/2  3/4
-----------------
2   -5    3/2  -5/4

Thus we have `2(x-1/2)1/2(2x^2-5x+3/2)` R`-5/4`

(** Multiply by 2 and 1/2: 2 to make the divisor the same as given in the problem, and 1/2 so as not tochange the expression **)

or `(2x-1)(x^2-5/2x+3/4)` R`-5/4`

So the quotient is `x^2-5/2x+3/4` and the remainder is `-5/4`

 

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

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We have to divide 2x^3 - 6x^2 + 4x - 2 by 2x - 1

2x - 1 | 2x^3 - 6x^2 + 4x - 2 | x^2 - 2.5x + 0.75

............2x^3 - x^2

-----------------------------------------

.......................-5x^2 + 4x - 2

.......................-5x^2 + 2.5x

-----------------------------------------

...................................1.5x - 2

...................................1.5x - 0.75

-----------------------------------------

.......................................... - 1.25

The required quotient is x^2 - 2.5x + 0.75 and the remainder is -1.25

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