Questions

• Manipulations of Simple Polynomials recognize polynomial as a special example of algebraic expressions recognize the meaning of the terminology involved

  給定$f(x)$是一個具有實數係數的多項式。如果$f(3)=f(9)$，那麼$f(2x-1)-f(x-2)$必須可以被

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• Identities explore the meaning of identities and distinguish between equations and identities discover and use the identities : difference of two squares; the perfect square expression; difference and sum of two cubes

  如果$\frac{i}{p-i^{2022}}+\frac{q}{i+q}$是一個實數，其中$p$和$q$是非零常數，那麼$q(p-1)$的最小值是

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• More About Polynomials Perform division of polynomials

  將多項式 \(4x^3 - 6x^2 + 2x - 8\) 除以多項式 \(2x - 4\)。商是什麼？

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• More About Polynomials Understand the remainder theorem

  將多項式 \( 2x^3 + 3x^2 - 5x + 6 \) 除以 \( x + 2 \)。

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• More About Polynomials Understand the remainder theorem

  給定多項式 \( P(x) = 2x^3 - 3x^2 + 4x - 5 \)，使用餘式定理來確定 \( P(x) \) 被 \( x - 2 \) 除時的餘數。

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• More About Polynomials Understand the remainder theorem

  給定多項式 \( P(x) = 2x^3 + ax^2 - 5x + 6 \)，已知當 \( P(x) \) 被 \( x - 2 \) 除時，餘數是 10。找出未知係數 \( a \) 的值。

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• More About Polynomials Understand the remainder theorem

  給定多項式 \( P(x) = 2x^3 + ax^2 + bx + 6 \)。當 \( P(x) \) 被 \( x-1 \) 除時，餘數是 5。當 \( P(x) \) 被 \( x+2 \) 除時，餘數是 -10。找出 \( a \) 和 \( b \) 的值。

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• More About Polynomials Understand the factor theorem

  給定多項式 \( P(x) = x^3 + ax^2 + bx + c \)，且 \( x-2 \) 是 \( P(x) \) 的一個因式，如果 \( P(x) \) 除以 \( x-2 \) 的商為 \( x^2 + 3x + 5 \)，求 \( c \) 的值。

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• More About Polynomials Understand the factor theorem

  考慮多項式 \( P(x) = x^3 + ax^2 + bx + c \)。已知 \( x-2 \) 是 \( P(x) \) 的一個因式。使用因式定理，如果 \( a = 3 \) 且 \( b = -4 \)，求 \( c \) 的值。

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

  找出多項式 \( P(x) = x^3 - 3x^2 + 3x - 1 \) 與 \( Q(x) = x^2 - 2x + 1 \) 的最大公因式（gcd）。

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