00:03
We're finding the quotient for 2x raised to the 5th pole minus 7x to the 4th pole minus 13 divided by 4x squared minus 6x plus 8.
00:20
Rewriting our numerator to have the pole of the x terms decreased by 1, it becomes 2x to the 5th pole minus 7x to the 4th pole plus 0x cubed plus 0x squared plus 0x minus 13 and that's all over 4x squared minus 6x plus 8 setting up our long division in which we have 4x squared minus 6x plus 8 being our divisal and our dividend being 2 x to the fifth pole minus 7 x raise to the fourth pole plus 0x cubed plus 0x squared plus 0x minus 13.
01:41
Dividing the first term of our dividend by the first term of our divisor gives us a half x cubed, multiplying 4x squared minus 6x plus 8 by a half x cubed gives us 2x raised cd fifth pole minus 3x raised cd fourth pole plus 4x cubed and we're subtracting all of that which leaves us with 0 negative 4x td 4th pole and negative 4x cubed bringing our 0x squared down we repeat the process in which we divide the first term of our dividend by the first term of our divisor that gives us negative x squared multiplying our divisor by negative x squared results in negative 4 x 3d 4x 3rd minus 6x cubed minus 8x squared oh, i'm sorry, negative 6x times negative x squared is positive 6x cubed.
03:30
Subtracting all of that would give us 0, negative 10x cubed, and positive 8x squared.
03:45
Bringing our 0x down, we repeat the process in which we divide the first term of our dividend.
04:06
By the first term of our divisor.
04:20
That results in negative 5 over 2x.
04:35
And we're multiplying or divisal by negative 5 over 2x, which results in negative 10 x cubed plus 15 x squared minus 20x and we're subtracting all of that.
05:27
That gives us 0, negative 7x squared, and positive 20x.
05:46
Carrying our negative 13 down, we repeat the process in which we divide the first term of our dividend by the first term of our divisor.
06:00
Doing that gives us negative 7 over 4.
06:03
Let's write that here...