SOLUTION: Two polynomials P and D are given. Use either synthetic or long division to divide P(x) by D(x), and express P in the form P(x) = D(x)

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Question 1148192: Two polynomials P and D are given. Use either synthetic or long division to divide
P(x) by D(x),
and express P in the form
P(x) = D(x) · Q(x) + R(x)
P(x) = 64x^5 − 16x^4 + 4x^2 − 4, D(x) = 4x^2 − 4x + 1
Answer by greenestamps(13198) (Show Source):
You can put this solution on YOUR website!

Synthetic division can only be used to divide a polynomial by a linear binomial; you need to use long division.

Do you not know how to do polynomial long division? Here is an example.
2x + 3 ------------------------- 3x^2 - 2x + 5 ) 6x^3 + 5x^2 + 6x + 20 6x^3 - 4x^2 + 10x ---------------------- 9x^2 - 4x + 20 9x^2 - 6x + 15 --------------- 2x + 5

6x^3+5x^2+6x+20, divided by 3x^2-2x+5, is 2x+3 with remainder 2x+5. Or, in the form required in your problem,

SOLUTION: Two polynomials P and D are given. Use either synthetic or long division to divide P(x) by D(x), and express P in the form P(x) = D(x) · Q(x) + R(x) P(x) = 64x^5 − 16