The Division Algorithm

makinsushi

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Oct 20, 2009
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I missed the lecture and notes for this chapter and I can't seem to make any sense of the notes my teacher provided online...

The book tells me:

"If f(x) and d(x) are polynomials such that d(x) does not equal 0, and the degree of d(x) is less than of equal to the degree of f(x), there exist unique polynomials q(x) and r(x) such that -

f(x) = d (x) q (x) + r

- where r(x) = 0 or the degree of r(x)is less than the degree of d(x). If the remainder is r(x) is zero, d(x) divides evenly into f(x)."

Which didn't help my cause at all.

The problem I'm trying to solve at this moment is:

"...express the function in the form f(x) = (x - k) q(x) + r for the given value of k, and demonstrate that f(k) = r."

Function:
f(x) = x^3 - x^2 - 14x + 11, where the value of k = 4

Please help!! I'm assuming we have a test on this material next week so I want to fully understand what I'm doing!!!
 
makinsushi said:
I missed the lecture and notes for this chapter and I can't seem to make any sense of the notes my teacher provided online...

The book tells me:

"If f(x) and d(x) are polynomials such that d(x) does not equal 0, and the degree of d(x) is less than of equal to the degree of f(x), there exist unique polynomials q(x) and r(x) such that -

f(x) = d (x) q (x) + r

- where r(x) = 0 or the degree of r(x)is less than the degree of d(x). If the remainder is r(x) is zero, d(x) divides evenly into f(x)."

Which didn't help my cause at all.

The problem I'm trying to solve at this moment is:

"...express the function in the form f(x) = (x - k) q(x) + r for the given value of k, and demonstrate that f(k) = r."

Function:
f(x) = x^3 - x^2 - 14x + 11, where the value of k = 4

Please help!! I'm assuming we have a test on this material next week so I want to fully understand what I'm doing!!!

Divide x^3 - x^2 - 14x + 11 by x-4 ---- using your favorite method
 
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