Questions

• More About Polynomials Perform division of polynomials Understand the remainder theorem

  已知$p$和$q$是常數。如果多項式$p x^{3}+q x^{2}-5 x+2$除以$x^{2}-3 x+2$，商為$Q(x)$，餘數為$12(x-1)$。求$Q(x)$。

  2024

• More About Polynomials Understand the remainder theorem Understand the factor theorem

  如果$a, b$和$c$是有理數，以下哪一項必定為真？ I. 如果$ac=bc$，則$a=b$。 II. 如果$a^{2}=b^{2}$，則$a=b$。 III. 如果$a^{3}=b^{3}$，則$a=b$。

  Premium 2024

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

  三個單項式的最大公因數和最小公倍數分別是$x y^{2}$和$18 x^{3} y^{4} z^{4}$。如果其中兩個單項式是$3 x y^{3}$和$9 x^{2} y^{4} z^{3}$，以下哪一個可能是第三個單項式？

  2024

• More About Polynomials Perform division of polynomials Understand the factor theorem

  若$(x-a)\left(x^{2}+a x+a^{2}\right)=b$，則$x=$

  2024

• More About Polynomials Perform division of polynomials Understand the factor theorem

  $8a^{3}+\frac{125}{a^{3}}=$

  Premium 2024

• More About Polynomials Understand the factor theorem Perform division of polynomials

  設 $P(x)$ 為一個多項式。如果 $x-k$ 是 $P(x)$ 的一個因式，那麼以下哪個多項式也必須有 $x-k$ 作為因式？ I. $2 P(x)$ II. $[P(x)]^{2}$ III. $P(2 x)$

  2024

• More About Polynomials Perform division of polynomials Understand the remainder theorem

  如果$m$和$n$是常數，使得$2mx(x+1)+\frac{x^{2}}{2}\equiv nx(x-4)+7x$，找出$m$和$n$的值。

  2024

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

  $x$、$3x^{3}$、$5x^{5}$、$7x^{7}$和$9x^{9}$的最小公倍數是

  2024

• Factorization of Simple Polynomials factorize polynomials by using identities including difference of two squares; perfect square expressions; difference and sum of two cubes

  $4+2mn-m^{2}-n^{2}=$

  Premium 2024

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

  如果$a, b$和$c$是非零常數，且$a x(b x+c)+5 \equiv 3 x^{2}+2 x+b c$，則$a: b: c=$

  2024