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polynomial division
- Thread starter teddy7
- Start date
Does the problem require using polynomial long division? It can be solved that way, but there is a somewhat easier way.I am finding it extremely confusing to use long division to find the other factor of x^4-a^4. One must be x-a but I do not exactly know how to find the other.
If anyone could help me out I would be very thankful!
(x^4-a^4)/(x-a)
Does the problem require using polynomial long division? It can be solved that way, but there is a somewhat easier way.
It needs to be solved using polynomial long division
Here is a hint:It needs to be solved using polynomial long division
\(\displaystyle Expand\ x^4 - a^4\ into\ x^4 + (0 * x^3a) + (0 * x^2a^2) + (0 * xa^3) - a^4.\)
Now divide (x - a) into the expanded polynomial, which MEANS THE SAME THING as the unexpanded one. Do you see why?
See how far you get with that. If you get an answer we can check it for you. If you get stuck, show us your work, and we shall help you get unstuck.
Bob Brown MSEE
Full Member
- Joined
- Oct 25, 2012
- Messages
- 598
I am finding it extremely confusing to use long division to find the other factor of x^4-a^4. One must be x-a but I do not exactly know how to find the other.
If anyone could help me out I would be very thankful!
(x^4-a^4)/(x-a)
Code:
[FONT=courier new]
[/FONT][FONT=courier new]| [/FONT][FONT=courier new] x^3 + ax^2
| ----------------------------------------------
[/FONT][FONT=courier new]|[/FONT][FONT=courier new](x-a) /x^4 + 0 + 0 ..... - a^4
[/FONT][FONT=courier new]| [/FONT][FONT=courier new]x^4 - a[/FONT][FONT=courier new]x^3
[/FONT][FONT=courier new]| [/FONT][FONT=courier new]----------
[/FONT][FONT=courier new]| [/FONT][FONT=courier new]ax^3 [/FONT][FONT=courier new]+ 0[/FONT][FONT=courier new]
[/FONT]Can you continue?
Here is a hint:
\(\displaystyle Expand\ x^4 - a^4\ into\ x^4 + (0 * x^3a) + (0 * x^2a^2) + (0 * xa^3) - a^4.\)
Now divide (x - a) into the expanded polynomial, which MEANS THE SAME THING as the unexpanded one. Do you see why?
See how far you get with that. If you get an answer we can check it for you. If you get stuck, show us your work, and we shall help you get unstuck.
x^3 + x^2a + xa^2 + a^3
--------------------------------------------------
(x-a)/x^4 + 0x^3a + 0x^2a^2 + 0xa^3 - a^4
x^4 - x^3a
----------
x^3a + 0x^2a^2
x^3a - x^2a^2
----------------
x^2a^2 + 0xa^3
x^2a^2 - xa^3
--------------
xa^3 - a^4
xa^3 - a^4
----------
0
Thank you so much for your help!!!!
Last edited: