Genber wiil evaluate an 8th degree polynomial in x at x=10 using the remainder theorem and synthetic division.how many coefficients of x will be written in the first row of the synthetic division procedure?

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08-08-2017
Mathematics

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Genber wiil evaluate an 8th degree polynomial in x at x=10 using the remainder theorem and synthetic division.how many coefficients of x will be written in the first row of the synthetic division procedure?

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Аноним Аноним · Answer 1 · 2017-08-14T15:42:05+02:00

An 8th-degree polynomial needs 9 terms that involve
x⁸, x⁷, ..., x¹, and x⁰.

x=10 implies that (x-10) is a factor of the polynomial according to the Remainder theorem.

Let the polynomial be of the form
f(x) = a₁x⁸ + a₂x⁷ + a₃x⁶ +a₄x⁵ + a₅x⁴ + a₆x³ + a₇x² + a₈x + a₉

The first few lines of the synthetic division are

10 | a₁ a₂ a₃ a₄ a₅ a₆ a₇ a₈ a₉ ( the first row has 9 coefficients)

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a₁

Answer:
The first row has 9 coefficients.