Question

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?

Answer 1

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)

    -----------------------------------------
      a₁

Answer:
The first row has 9  coefficients.