Questions

• More About Polynomials Understand the concepts of the greatest common divisor and the least common multiple of polynomials

  給定多項式 \( P(x) = 2x^3 - 4x^2 \)，\( Q(x) = 4x^2 - 8x \)，和 \( R(x) = 6x^3 - 12x^2 \)，找出這些多項式的最大公因數 (GCD)。

  2024

• More About Polynomials Understand the concepts of the greatest common divisor and the least common multiple of polynomials

  考慮多項式 \( P(x) = x^3 - 3x^2 + 2x \) 和 \( Q(x) = x^2 - x \)。找出這些多項式的最小公倍數（LCM）。

  2024

• More About Polynomials Perform addition, subtraction, multiplication, and division of rational functions

  給定有理函數 \( \frac{2x}{x+1} \) 和 \( \frac{3}{x-1} \)，找出它們相加的結果。

  2024

• More About Polynomials Perform addition, subtraction, multiplication, and division of rational functions

  考慮有理函數 \( f(x) = \frac{2x + a}{x + 1} \) 和 \( g(x) = \frac{3x + b}{x - 1} \)。執行這兩個有理函數的加法並簡化結果。

  2024

• More About Polynomials Perform addition, subtraction, multiplication, and division of rational functions

  考慮以下有理函數：\[ f(x) = \frac{2x^2 + 3x - 2}{x + 1} \]\[ g(x) = \frac{x^2 - 1}{x - 1} \]\[ h(x) = \frac{3x + 2}{x + 2} \]執行以下操作並簡化結果：\[ \left( f(x) + g(x) \right) \times h(x) \]

  2024

• More About Equations Use the algebraic method to solve simultaneous equations in two unknowns, one linear and one quadratic

  給定線性方程式 \( y = 2x + 3 \) 和二次方程式 \( y = x^2 + kx + 1 \)，找出 \( k \) 的範圍，使得該系統有實根。

  2024

• More About Equations Use the algebraic method to solve simultaneous equations in two unknowns, one linear and one quadratic

  解以下方程組以求 \( x \) 和 \( y \)：1. \( y = x^2 + 2x + 1 \)2. \( 2x + y = 5 \)

  2024

• More About Equations Use the algebraic method to solve simultaneous equations in two unknowns, one linear and one quadratic

  解以下方程組以求 \(x\) 和 \(y\):1. \( y = x^2 + 3x + 2 \)2. \( y = 2x + 4 \)

  2024

• More About Equations Solve equations (including fractional, exponential, logarithmic, and trigonometric equations) which can be transformed into quadratic equations

  解以下分數方程式以求 \(x\)：\[\frac{2x + 3}{x - 1} - \frac{x + 1}{x + 2} = 1\]

  2024

• More About Equations Solve equations (including fractional, exponential, logarithmic, and trigonometric equations) which can be transformed into quadratic equations

  在\(0^\circ \leq x < 360^\circ\)的區間內求解下列三角方程式的\(x\)值：

  2024