グローバルビジネスで役立つ数学（36）三次多項式の因数分解（英語版）

Hi there!

First of all, read the following telephone call by an American exporter.

――”Hi, Mr. Yoshida. Sorry to call you late. I wanted to call you earlier, but when I checked into
　　the hotel, I got a memo and realized that one of our major clients went belly up and had to
　　put out some fires.”

It was an authentic story when I was working at a trading company. You may understand the call easily when I replace the phrase “went belly up” with “went into bankruptcy” or “went under.” We never know what happens tomorrow in the dog-eat-dog corporate world.

“Factoring” has recently been catching on as a contingency plan to avoid chain-reaction bankruptcies caused by one of your business partners. This type of financial transaction or debtor finance in which a business sells its accounts receivable to a third party at a discount will increasingly be taken for granted as risk management.

Today, let me try “factoring” a cubic function instead of a small and medium-sized company’s accounts receivable.

Factor the following cubic polynomial.
\(2a^{3} + 4a^{2}b – 2a – 4b\)

Here is my solution to the problem.

\(2a^{3} + 4a^{2}b – 2a – 4b\)
\(= 2(a^{3} + 2a^{2}b – a – 2b)\)
\(= \displaystyle\left\{a(a^{2} -1) + 2b(a^{2} – 1)\right\}\)
\(= 2(a^{2} – 1)(a + 2b)\)
\(= 2(a + 1)(a – 1)(a + 2b)\)

Can you take this factoring to the bank?

Stay tuned, and expect to see my next post.

Keep well.

Frank Yoshida

￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣
【グローバルビジネスで役立つ数学】でもっと学習する b＾＾)
【参考図書】『もう一度高校数学』（著者：高橋一雄氏）株式会社日本実業出版社
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