Please help me
Divide.
(9x^3-10+19+6x^4)/(-2x^2+3x-3)
Write your answer in the form Q(x)+ R(x)/ -2x^2+3x-3,
where Q(x) is the quotient and R(x) is the remainder.
First rearrange and simplify the numerator to:
6x^4 + 9x^3 + 9
Just divide as your would with any long division problem.
If you post your answer I can tell you if you are correct.
Is there something in particular you do not understand?
Just not good at division
I'll try, but the formatting here doesn't allow for easy alignment of columns.
xxxxxxxxxxxxx-3x^2 - 9x - 9
-2x^2+3x-3 |6x^4 + 9x^3 + 0x^2 + 0x +9
------------6x^4 - 9x^3 + 9x^2
subtraction-------18x^3 - 9x^2
------------------18x^3 - 27x^2 + 27x
subtraction-------------18x^2 - 27x + 9
------------------------18x^2-27x + 27
subtractionxxxxxxxxxxxxxxxxxxxxxxx -18
Answer in the form
Q(x)+ R(x)/ -2x^2+3x-3,
-3x^2 - 9x - 9 + -18/(-2x^2 + 3x - 3)
I don't know how you will follow this because of the formatting.
Ok I will try to figure it out and ask if I need anymore questions. thanks for your help
You're welcome and good luck :).
To divide the given polynomial, we can use long division.
Step 1: Start by setting up the long division problem. Place the dividend (9x^3 - 10 + 19 + 6x^4) inside the division bracket, and the divisor (-2x^2 + 3x - 3) outside the bracket.
_________________________
-2x^2 + 3x - 3 | 6x^4 + 9x^3 - 10 + 19
Step 2: Divide the highest degree term of the dividend by the highest degree term of the divisor. In this case, divide 6x^4 by -2x^2 to get -3x^2.
-3x^2
_________________________
-2x^2 + 3x - 3 | 6x^4 + 9x^3 - 10 + 19
Step 3: Multiply the divisor (-2x^2 + 3x - 3) by the quotient (-3x^2) and subtract the result from the dividend.
-3x^2(-2x^2 + 3x - 3) = 6x^4 - 9x^3 + 9x^2
Subtracting: 9x^3 - (-9x^3) = 18x^3
-10 - 9x^2 = -9x^2 - 10
+19 - 0 = 19
18x^3 - 9x^2 - 10 + 19
_________________________
-2x^2 + 3x - 3 | 6x^4 + 9x^3 - 10 + 19
Step 4: Repeat steps 2 and 3 with the new dividend (18x^3 - 9x^2 - 10 + 19), bringing down the next term.
-3x^2 - 6x + 6
_________________________
-2x^2 + 3x - 3 | 6x^4 + 9x^3 - 10 + 19
- (6x^4 - 3x^3 + 3x^2)
_______________________
6x^3 - 13x^2 - 10 + 19
6x^3 - 13x^2 - 10 + 19
_________________________
-2x^2 + 3x - 3 | 6x^4 + 9x^3 - 10 + 19
Step 5: Repeat steps 2 and 3 with the new dividend (6x^3 - 13x^2 - 10 + 19), bringing down the next term.
-3x^2 - 6x + 6 - (12x^2 - 6x + 6)
_________________________
-2x^2 + 3x - 3 | 6x^4 + 9x^3 - 10 + 19 - (6x^4 - 3x^3 + 3x^2)
- (12x^2 - 6x + 6)
_______________________
-13x^2 + 4
-13x^2 + 4
_________________________
-2x^2 + 3x - 3 | 6x^4 + 9x^3 - 10 +19
Step 6: There are no more terms left to bring down. The result after dividing is -3x^2 - 6x + 6 with a remainder of -13x^2 + 4.
Therefore, the answer in the requested form is:
Q(x) = -3x^2 - 6x + 6
R(x) = -13x^2 + 4
So, the final answer is (-3x^2 - 6x + 6) + (-13x^2 + 4) / -2x^2 + 3x - 3.