Long Division of Polynomials 05:07 minutes

Video Transcript

Transcript Long Division of Polynomials

“The World --- will end on ---th 30--! No more --- for ---- of the year! ---” Scientists have intercepted a cryptic radio message and rush to save mankind. Luckily, the scientists’ robot was able to detect a code embedded in the message. The message is coded in math and tells them the exact day, month and year when the world will end. To solve the riddle and save the world, the scientists must use their knowledge of long division of polynomials.

The long division of polynomials

These are the equations the Robot overheard. The result of the first equation will tell us the month and date while the combined result of the next two equations will give us the year. Let's get started.

The first part of the message is the month and date: Long division with polynomials is no different than long division with numbers. Let's look at the easy example 428 divided by 6. In this example we first look at how many times 6 goes into 4. Since 6 does not go into 4 we have to look at the next digit. How many times does 6 go into 42. 6 goes into 42 7 times. Now multiply 7 times 6 which gives us 42. We subtract 42 from 42 and get zero. In the same way, we should ask ourselves, "How many times does 'x' go into x squared?" x' times 'x' gives us 'x' squared, so we write 'x'. Next, we multiply 'x' times 'x' plus 3. We subtract this result from the polynomial under the long division symbol. 'x' squared minus 'x' squared gives us zero. Negative 17x minus 3x gives us negative 20x.

Now, just like with regular long division, we bring the next number down and repeat the process of asking the question - How many times does the divisor go into the dividend? - until there are no numbers left. In this example, six goes into eight exactly one time. Then, we multiply 1 times 6 and get 6. This 6 is subtracted from the 8 and we're left with 2.

In the same way, we bring the negative 51.2 down to get the expression -20x - 51.2. Now we have to see how many times x goes into -20x. It goes in -20 times, which we write here. Then, we multiply -20 by 'x' plus 3 to get -20x minus 60. This is subtracted from the binomial negative 20x minus 51.2. This gives us 8.8.

What do we do with this? We know it's a remainder, but how do we know how many times 'x' goes into it?!? We don't even know what 'x' is! Don't worry, just like long division with numbers, you write the remaining numbers over the divisor. Normally, you have to simplify your fraction, if you can. But when your divisor has a variable, you can't simplify any further, so you're done! Remember, this remainder 8.8 tells us the month and date of the End of the world.

The second part of the message reveals the first two numbers of the year. Just like before, we ask, "how many times does 'x' go into 'x' squared?" We multiply our answer by our dividend, subtract and bring down the next term. We repeat the process. And finally, write the leftovers over our dividend, giving us the remainder. This remainder is the first 2 digits of the year the world will end. The scientists are almost done! Once they find out the last two digits of the year, they can save the world!

The third and final part of the message reveals the last two numbers of the year. Even though the scientists have to hurry, they stick to the plan and go step by step. * bring the next term down * multiply * subtract * and write the dividend over the divisor, and there you have it: the remainder!

So 1 and 6 are the last two digits of the year. With the code cracked, the scientists rush to enter the date into their time machine “8.8.3016”. That's strange, it sure doesn't look like the world's about to end. “The World Series will end on August 8th, 3016! No more games for the remainder of the year! Get your tickets now!.” Oh! Game 7 of the World Series!!!