Question

Thu gọn và sắp xếp luỹ thừa của biến

f(x)= 2x^2 -x +3 -4x -x^4
g(X)= 4X^2 + 2X + X^4 -2 + 3X

Answer 1

To simplify the expressions and arrange the terms by their degree, we can write:

$\longrightarrow\sf\textbf\:f(x)\:= -x^4\:+\:2x^2\:-\:5x\:+\:3$

$\longrightarrow\sf\textbf\:=\:-x^4 + 2x^2 - x - 4x + 3$

$\longrightarrow\sf\textbf\:=\:-x(x^3 - 2x + 1) - 4x + 3$

$\longrightarrow\sf\textbf\:g(x)\:=\:x^4 + 4x^2 + 2x + 1$

$\longrightarrow\sf\textbf\:x^4 + 4x^2 + 2x + 1 - 2 + 2$

$\longrightarrow\sf\textbf\:x^4 + 4x^2 + 2x - 1 + 2$

$\longrightarrow\sf\textbf\:x^4 + 4x^2 + 2x - 1 + 2$

$\longrightarrow\sf\textbf\:x^4 + 4x^2 + 2x + 1 - 2$

$\longrightarrow\sf\textbf\:(x^2 + 1)^2 - 2$

Therefore, we can express the simplified forms of ${\sf{\textbf{f(x)}}}$ and ${\sf{\textbf{g(x)}}}$ as:

$\longrightarrow\sf\textbf\:f(x)\:=\:-x(x^3 - 2x + 1) - 4x + 3$

$\longrightarrow\sf\textbf\:g(x)\:=\:(x^2 + 1)^2 - 2$

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