🚂 多项式：一列按次排队的项🚂 Polynomials: A Train of Terms Lined Up by Degree
上一片我们忙着拆式子。这一片回头看看被拆的这类式子：3x²+2x−5、x²+5x+6。它们有个共同的名字——多项式。它们像一列火车，每节车厢就是一个"项"。Last leaf we were busy splitting expressions apart. This leaf looks back at the kind we split: 3x²+2x−5, x²+5x+6. They share one name — polynomials. Think of them as a train, and each car is a "term".
第 1 步：多项式 = 一列项小火车Step 1: A polynomial is a train of terms
先认识这列车：每节车厢就是一个"项"，项与项之间用加号连起来。First meet the train: each car is one "term", and terms are joined by plus signs.
3x²+2x−5 像一列三节车厢的小火车：车厢是 3x²、2x 和 −5。每个"项"都是"数字 × 字母"的积（−5 可以看成 −5 × 1）。整列车就叫多项式。3x²+2x−5 is a little train with three cars: 3x², 2x and −5. Every term is a number × letter product (−5 counts as −5 × 1). The whole train is called a polynomial.
车厢的等级怎么定？看字母头顶的那个小数字（指数）。How is a car's rank decided? Look at the little number above the letter — the exponent.
第 2 步：次数 = 最高次车厢的等级Step 2: The degree is the top car's rank
3x² 的 x 头顶是 2，是 2 次；2x 是 1 次；−5 没有字母，是 0 次。整列车的次数取最高——2 次，所以叫"二次多项式"。The x in 3x² carries a 2, so that car is degree 2; 2x is degree 1; −5 has no letter, so degree 0. The train takes the highest — degree 2 — so it is a "degree-2 polynomial".
车厢乱停会看不清结构——它们习惯从高次到低次排好队。Cars parked at random hide the structure — the habit is to line them up from highest power to lowest.
第 3 步：按降幂排队Step 3: Line up, highest power first
把 5+2x²−3x 整队：2x²（2 次）→ −3x（1 次）→ 5（0 次），写成 2x²−3x+5。降幂排队后，次数一眼看出，后面的计算也更顺手。Line up 5+2x²−3x: 2x² (degree 2) → −3x (degree 1) → 5 (degree 0), written as 2x²−3x+5. Once sorted, the degree is obvious at a glance and later calculations go smoothly.
🎮 你来当检票员（30 秒）🎮 Your turn: check the tickets (30 seconds)
道理讲完了。4 道关卡：点出次数、找出最高次车厢、把车厢排队、说出名字。Theory done. Four levels: name the degree, spot the highest-power car, line the cars up, and say what the train is called.
一句话记住它：多项式 = 项的火车；次数看最高次；习惯按降幂排队。Remember it in one line: a polynomial is a train of terms; the degree is the highest power; line the terms up from high to low.
项：数字 × 字母的积，如 3x²、2x、−5，用加号相连Terms: number × letter products such as 3x², 2x, −5, joined by plus signs次数：看最高次项，3x²+2x−5 是二次多项式Degree: the highest-power term wins — 3x²+2x−5 has degree 2降幂排队：从高次排到低次，5+2x²−3x 写成 2x²−3x+5Sort by descending power: 5+2x²−3x becomes 2x²−3x+5
内容参考 OpenStax 等公开教材，多来源核对 · AI 生成、人工审核 · 发现错误欢迎指正，帮这片叶子长得更好。Based on OpenStax and other open textbooks, cross-checked across sources · AI-generated, human-reviewed · Spotted a mistake? Tell us — help this leaf grow.
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