SUEC 高中 Adv Maths (Remainder, Factor Theorem)
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The document discusses the remainder theorem and factor theorem. The remainder theorem states that the remainder of a polynomial division is equal to evaluating the dividend polynomial at the point of the divisor polynomial. The factor theorem states that if a polynomial f(x) has a factor of (x - a), then f(a) must equal 0. The document provides examples of applying these theorems to polynomial functions.
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(2) Methods are described for finding the angles between two tangent lines to a circle based on their slopes. Examples are given of solving systems of equations to find the points where tangent lines intersect.
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- Distance ratios used to define loci and find their equations
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SUEC 高中 Adv Maths (Earth as Sphere) (Part 1).pptx
The document provides steps for calculating time differences and longitude differences between two locations:
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Visual - various maths sites (credits to original creator)
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Visual - various maths sites (credits to original creator)
Questions - Dong Zong's Textbook
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- 1. 𝒇 𝒙 = (𝒙 − 𝒂) ∙ 𝑸 𝒙 + 𝑹(𝒙) a a 𝒇 𝒙 = 𝒈 𝒙 ∙ 𝑸 𝒙 + 𝑹(𝒙) 𝑳𝒆𝒕 𝒙 = 𝒂 𝒇 𝒂 = 𝑹(𝒙) 余数定理
- 2. 𝒑𝒈 𝟖𝟗 − 𝟗𝟏 余数定理 𝒓𝒆𝒎𝒂𝒊𝒏𝒅𝒆𝒓 𝒕𝒉𝒆𝒐𝒓𝒆𝒎 3
- 3. 𝒑𝒈 𝟗𝟏 余数定理 𝒓𝒆𝒎𝒂𝒊𝒏𝒅𝒆𝒓 𝒕𝒉𝒆𝒐𝒓𝒆𝒎
- 4. 𝒑𝒈 𝟗𝟐 余数定理 𝒓𝒆𝒎𝒂𝒊𝒏𝒅𝒆𝒓 𝒕𝒉𝒆𝒐𝒓𝒆𝒎 𝟑𝟔 𝟏 𝟗 𝟏𝟓𝟎 − 𝟑 𝟏 − 𝟐 − 𝟔𝟎 𝒉 = − 𝟒 𝒌 = − 𝟐 𝒙 + 𝟑 − 𝟒𝒙 + 𝟕 𝒂 = − 𝟗 𝒃 = 𝟒
- 5. 𝒇 𝒙 = (𝒙 − 𝒂) ∙ 𝑸 𝒙 + 𝑹(𝒙) a a 𝒇 𝒙 = 𝒈 𝒙 ∙ 𝑸 𝒙 + 𝑹(𝒙) 𝑳𝒆𝒕 𝒙 = 𝒂 𝒇 𝒂 = 𝑹(𝒙) 余数定理 a 因试定理 a 𝒊𝒇 𝒇 𝒂 = 𝟎 𝒙 − 𝒂 𝒊𝒔 𝒂 𝒇𝒂𝒄𝒕𝒐𝒓 𝒐𝒇 𝒇(𝒙) 𝑹 𝒙 = 𝟎
- 6. 𝒑𝒈 𝟗𝟑 − 𝟗𝟒 𝒇𝒂𝒄𝒕𝒐𝒓 𝒕𝒉𝒆𝒐𝒓𝒆𝒎 因试定理
- 7. 𝒑𝒈 𝟗𝟔 𝒇𝒂𝒄𝒕𝒐𝒓 𝒕𝒉𝒆𝒐𝒓𝒆𝒎 因试定理 𝐘 𝐘 𝐘
- 8. 𝒑𝒈 𝟗𝟒 − 𝟗𝟓 𝒇𝒂𝒄𝒕𝒐𝒓 𝒕𝒉𝒆𝒐𝒓𝒆𝒎 因试定理
- 9. − 𝟒 𝒌 = 𝟐 𝒂 = 𝟏 𝒃 = − 𝟐𝟕 𝒑𝒈 𝟗𝟔 𝒇𝒂𝒄𝒕𝒐𝒓 𝒕𝒉𝒆𝒐𝒓𝒆𝒎 因试定理 − 𝟑 − 𝟏 𝒎 = − 𝟗 𝒏 = 𝟕 𝒂 = 𝟏𝟐 𝒄 = − 𝟏𝟕 𝒌 = − 𝟐 𝑹 𝒙 = − 𝟐𝟎 𝒂 = − 𝟔𝟐 𝒃 = −𝟏𝟎𝟒 𝒎 = 𝟏 𝒏 = 𝟓 𝒇 𝒚 = 𝒚 𝒚 + 𝟏 𝟐 (𝟑𝒚 − 𝟕)
- 10. 𝒑𝒈 𝟗𝟓 𝒇𝒂𝒄𝒕𝒐𝒓 𝒕𝒉𝒆𝒐𝒓𝒆𝒎 因试定理
- 11. 𝒑𝒈 𝟗𝟔 𝒇𝒂𝒄𝒕𝒐𝒓 𝒕𝒉𝒆𝒐𝒓𝒆𝒎 因试定理 𝒇 𝒙 = 𝟐𝒙𝟐 + 𝟐𝒙 − 𝟒 𝒇 𝒙 = 𝒌(𝒙 − 𝟏)(𝒙 + 𝟐) 𝒇 𝒙 = 𝒙 − 𝟑 𝒙 + 𝟓 𝒙 − 𝟐 = 𝒙𝟑 − 𝟏𝟗𝒙 + 𝟑𝟎
Editor's Notes
- https://slideplayer.com/slide/14396997/
- https://www.onlinemathlearning.com/dividing-polynomials-synthetic-division.html linear factor – cannot be factored further
- https://www.onlinemathlearning.com/dividing-polynomials-synthetic-division.html linear factor – cannot be factored further
- https://www.onlinemathlearning.com/dividing-polynomials-synthetic-division.html linear factor – cannot be factored further
- https://slideplayer.com/slide/14396997/