Math Is Fun Forum

Kiran

Member

Registered: 2006-11-15

Posts: 177

need more help

Use the remainder theorem to evaluate 2x^3 - 5x^2 + 2x + 5 when x = -2

ok i only got up to here i dont know what else to do

p(-2)

-2 |  2  -5  2  5
___      -5

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mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: need more help

For this question you need to divide (2x³ - 5x² + 2x + 5) by (x+2), using algebraic division.

(2x³ - 5x² + 2x + 5)/(x+2)
Split the x² term: (2x³ + 4x² - 9x² + 2x + 5)/(x+2)
Factorise partially: 2x² + (-9x² + 2x + 5)/(x+2)
Split the x term: 2x² + (-9x² - 18x + 20x + 5)/(x+2)
Factorise partially: 2x² - 9x + (20x+5)/(x+2)
Split the constant: 2x² - 9x + (20x + 40 - 35)/(x+2)
Factorise partially: 2x² - 9x + 20 - 35/(x+2)

And now, by the remainder theorem, we know that the function has a value of -35, when x = -2.

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krassi_holmz

Real Member

Registered: 2005-12-02

Posts: 1,905

Re: need more help

mathsy's right.
With horner's scheme (i don't know exactly how's in English): ( changing the sign:)
   | 2  -5   2     5
2 | 2  -9  20  -35 ->remainder;

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