I am totally lost!
(3x^4--8x^2 -3x-3) / (x^2-3)
You have to do polynomial long division.
I can't layout the problem here because of the alignment of columns and such.
See this website. It explains in detail how to do this.
I'll check your answer if you post it.
Good luck :)
http://www.purplemath.com/modules/polydiv2.htm
Just checking to see if I got this right.
Thanks,
(3x^4--8x^2 -3x-3) / (x^2-3)
3x^2+1 remainder -3x
Don't worry, I can help you with that!
To simplify the expression (3x^4 - 8x^2 - 3x - 3) / (x^2 - 3), we can use the long division method. Here's how:
Step 1: Divide the first term of the numerator (3x^4) by the first term of the denominator (x^2). So, 3x^4 / x^2 = 3x^2.
Step 2: Multiply the result from Step 1 (3x^2) by the entire denominator (x^2 - 3). So, 3x^2 * (x^2 - 3) = 3x^4 - 9x^2.
Step 3: Subtract the result from Step 2 (3x^4 - 9x^2) from the numerator (3x^4 - 8x^2 - 3x - 3). This gives us (-8x^2 - 3x - 3).
Step 4: Bring down the next term from the numerator, which is -3x. Now we have (-8x^2 - 3x - 3 - 3x).
Step 5: Divide the first term of the new expression (-8x^2) by the first term of the denominator (x^2). So, -8x^2 / x^2 = -8.
Step 6: Multiply the result from Step 5 (-8) by the entire denominator (x^2 - 3). So, -8 * (x^2 - 3) = -8x^2 + 24.
Step 7: Subtract the result from Step 6 (-8x^2 + 24) from the expression obtained in Step 4 (-8x^2 - 3x - 3 - 3x). This gives us (-6x - 27).
Step 8: Bring down the next term from the numerator, which is -27. Now we have (-6x - 27 - 27).
Step 9: Divide the first term of the new expression (-6x) by the first term of the denominator (x^2). So, -6x / x^2 = -6/x.
Step 10: Multiply the result from Step 9 (-6/x) by the entire denominator (x^2 - 3). So, -6/x * (x^2 - 3) = -6x - 18/x.
Step 11: Subtract the result from Step 10 (-6x - 18/x) from the expression obtained in Step 8 (-6x - 27 - 27). This gives us - (-27 - 18/x).
The final simplified expression is -27 - 18/x.