Question

[Trương Ngọc Linh]

Tìm GT đa thức sau :

a) \(A\left(x\right)=x^{15}+5^{14}+3x^3-24\) biết x + 5 = 0

b) \(B\left(x\right)=\left(x^{2024}+7x^{2023}+1\right)^{2024}\) biết x = -7

Answer 1

[Nguyễn Lê Phước Thịnh]

\(A\left(x\right)=x^{15}+5x^{14}+3x^3-24\)

\(=x^{14}\left(x+5\right)+3x^3+375-399\)

\(=3\left(x^3+125\right)-399\)

\(=3\left(x+5\right)\left(x^2-5x+25\right)-399\)

=-399

\(B\left(x\right)=\left(x^{2024}+7x^{2023}+1\right)^{2024}\)

\(=\left[x^{2023}\left(x+7\right)+1\right]^{2024}\)

\(=\left[x^{2023}\left(-7+7\right)+1\right]^{2024}=1^{2024}=1\)