Polynomials:Dividing

Hey everyone! In case you missed today's math class, forgot some of the notes or whatever your reason may be, here's a quick recap of today's lesson.

Division

16/2=8 Easy enough right?
4x/4 is done the same way. 4x/4 is 1x or x(If it's 1x or 1y or 1_ you don't have to include the "1")

can also be written as which equals 2x+1.

Now for the grade 10 math stuff:
To make this a little easier, let's write it as

Now I'm pretty sure that you've done long division before. This question is done just like normal long division except that now there are variables.


*Please remember that when you write down the question, the numbers have to be in descending order according to powers of x (ex. x³ then x² then x then number with no variable) or else your answer will be wrong.*


Now what you do is look at just the "x". What do you need to multiply "x" by to get x³? The answer is x² . So now you put x² on top like so:


Now you have to multiply the whole divisor (x+1) by x² which should work out to x³+x² . Now subtract that from the equation as you would in a regular long division question:

Now bring down the next term and repeat.

What do you multiply x by to get 3x² ? 3x! Then multiply: 3x(x+1) [which turns out to be 3x² +3x], subtract it from the equation again and bring down the next term:

Now how many times does "x" go into 4x? 4! Now, once again multiply 4(x+1) [which is 4x+4] ,subtract and.........

..........you now have your answer! YAY!!

Now, to check if this is right, take the divisor(x+1), multiply it by the quotient (x²+3x+4) and add the remainder (which happens to be 0). If you get the original polynomial (x³+4x²+7x+4) then it's right!

Now a couple of extra points. PLEASE READ THESE!

If there is a remainder after this step:

Leave it as R _ like in a regular long division question.

If there is a term "missing" like in the example x⁴+3x²-7x+4 (an "x³" is missing), add it in as +0x³ and put it in the right place(in between x⁴ and +3x²). If you don't do this, your answer will not turn out right!

If the divisor has a negative integer like x-2, don't forget that when you subtract a negative integer, you "flip" the sign and add. Ex. 10-(-12)=10+12=22

Finally, here was the homework assignment:

Exercise 3

Questions 1-12

You don't have to check your answers (just in case you were wondering).

I hope this helps! =]

~PJ

OH! I almost forgot! The next scribe is...........(drum roll) kimberly! Enjoy!