Cho đa thức: f(0) = x^20-10x^10 + 10x^18-10x^7+….+ 10x^2-10x + 1. Tính f(9) 18/10/2021 Bởi Mary Cho đa thức: f(0) = x^20-10x^10 + 10x^18-10x^7+….+ 10x^2-10x + 1. Tính f(9)
Ta có $f(x) = x^{20} – 10x^{19} + 10x^{18} – 10x^{17} + \cdots + 10x^2 – 10x + 1$ $= x^{20} – 9x^{19} -x^{19} + 9x^{18} + x^{18} – 9x^{17} -x^{17} + \cdots + x^2 – 9x – x + 9 -8$ $= x^{19} (x-9) – x^{18} (x-9) + x^{17}(x-9) – \cdots + x(x-9) -(x-9) – 8$ $= (x-9)(x^{19} – x^{18} + x^{17} – \cdots + x – 1) – 8$ Khi đó $f(9) = 0 (x^{19} – x^{18} + x^{17} – \cdots + x – 1) – 8$ $= -8$Vậy $f(9) = -8$. Bình luận
Ta có
$f(x) = x^{20} – 10x^{19} + 10x^{18} – 10x^{17} + \cdots + 10x^2 – 10x + 1$
$= x^{20} – 9x^{19} -x^{19} + 9x^{18} + x^{18} – 9x^{17} -x^{17} + \cdots + x^2 – 9x – x + 9 -8$
$= x^{19} (x-9) – x^{18} (x-9) + x^{17}(x-9) – \cdots + x(x-9) -(x-9) – 8$
$= (x-9)(x^{19} – x^{18} + x^{17} – \cdots + x – 1) – 8$
Khi đó
$f(9) = 0 (x^{19} – x^{18} + x^{17} – \cdots + x – 1) – 8$
$= -8$
Vậy $f(9) = -8$.