What is the remainder of (3x^2 - 18x + 4)/(x^2 + 4)

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The remainder of `(3x^2 - 18x + 4)/(x^2 + 4)` has to be determined.

x^2 + 4 | 3x^2 - 18x + 4 | 3

...............3x^2 + 12

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

........................-18x - 8

The remainder when 3x^2 - 18x + 4 is divided by x^2 + 4 is -18x - 8

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tonys538 | Student, Undergraduate | (Level 1) Valedictorian

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The remainder when (3x^2 - 18x + 4) is divided by (x^2 + 4) is required.

3x^2 - 18x + 4

= 3*(x^2 + 4) - 18x - 12 + 4

= 3*(x^2 + 4) - 18x - 8

Now 3*(x^2 + 4) is a factor of x^2 + 4. The rest is the remainder as the highest power of x in -18x - 8 is lower than the highest power of x in the denominator.

The required remainder is -18x - 8

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