factored的音標為["f?kt?d]，基本翻譯為“因數分解的；因子的；分解的”，速記技巧為“fact（事實）＋or（人）＋ed（的）＝因數分解的”。

factored這個詞的英文詞源可以追溯到拉丁語詞根“factor”和“factorium”，意為“因子”或“因素”。它的變化形式主要有“factorize”、“factorial”和“factorization”等。

相關單詞：

factorize：意為“因子化”，指將一個復雜的問題分解為更小的、更容易處理的子問題。

factorial：意為“因子的”，是數學中的一個概念，用于表示一個數的所有因子（包括1但不包括它本身）的乘積。

factorization：意為“因子的化”，指將一個復雜問題分解為因子的過程或方法。

factored這個詞在英語中常用于數學、經濟學等領域，特別是在計算數學中，將問題分解為更小的組成部分，以便更有效地解決它們。這種分解方法有助于提高解決問題的效率，降低復雜性。

常用短語：

1. factored out （因式分解）

2. factor in （考慮因素）

3. factor out （排除因素）

4. prime factors （質因數）

5. factorial （階乘）

6. factoring （因式分解法）

7. factoring in （考慮其他因素）

雙語例句：

1. The problem has been factored out and can be solved easily.

這個問題已經因式分解，可以輕松解決。

2. When making decisions, always factor in the long-term consequences.

做決定時，總是要考慮長期后果。

3. The prime factors of a number are its divisors.

一個數的質因數就是它的除數。

4. Factoring is a useful tool for solving equations and inequalities.

因式分解是解決方程和不等式的一個有用的工具。

5. We need to factor in the cost of transportation when planning our trip.

在計劃旅行時，我們需要考慮交通費用。

6. The problem cannot be solved without factoring in the unknown variable.

如果不考慮未知變量，這個問題就無法解決。

7. The factorial of 5 is 120, which is a very large number!

5的階乘是120，這是一個非常大的數字！

英文小作文：

Factors and Their Importance

Factors are essential components that influence various aspects of our lives, from our health to our academic performance. Factors can be positive or negative, and they can vary in importance depending on the situation. Understanding factors and how they interact is crucial for making informed decisions and achieving success.

For example, when it comes to studying for a test, factors such as time constraints, study materials, and motivation play a significant role in our performance. Factors such as our health and sleep patterns can also affect our ability to concentrate and perform well in schoolwork. On the other hand, factors such as peer pressure and negative attitudes can have a negative impact on our academic performance and success.

In addition to academic factors, there are also financial factors that can affect our lives. For instance, access to education, financial aid, and scholarships can play a significant role in our ability to pursue higher education and succeed in our career goals. Similarly, social factors such as family support, peer relationships, and community resources can also influence our success and well-being.

In conclusion, factors are essential components that influence our lives in numerous ways. Understanding and managing these factors is crucial for achieving success and well-being. By taking into account various factors, we can make informed decisions and take appropriate actions to achieve our goals and dreams.