How Do You Solve Complex Polynomial Long Division Problems?

In summary, the conversation is about dividing polynomials using long division. The process involves using the expanded forms of the polynomials and finding the correct partial quotient. There may be a remainder that needs to be accounted for in the final result. It is important to use all terms of the divisor in order to get the correct answer. It is also suggested to check the result by multiplying it with the divisor to ensure it is equivalent to the original dividend.
  • #1
acuraintegra9
7
0
Divide the polynomials by using long division.
(-9x^6+7x^4-2x^3+5)/(3x^4-2x+1)



When I attempted it I started by pulling using 3x^2 . multiplied that by the (3x^4-2x+1) and from there I had to use a fraction of 7/3 or something and then couldn't divide into x cubed.


If anyone can help me that would help out so much.. All the examples in my book, that we talked about in class, and the ones online are mostly simple ones that work out evenly, are not that high of exponents etc.
 
Physics news on Phys.org
  • #2
Use the polynomials in their expanded forms. Your first partial quotient should be -3x^2. Multiply this by the divisor and subtract the result from the dividend to obtain your revised dividend in order to continue the process.

(note carefully, "-3x^2" means "negative three times x squared")
 
Last edited:
  • #3
I did that much, but then the tricky part is when I add it in what's left after eliminating the x6 and x5 I get .. 7x^4-8x^3+3x^2+0x +5

dont know what to do from there.. do I have to multiply the 3x^4 by some sort of fraction to get it to equal to 7 to cancel out..
 
  • #4
please help! not sure what to do .. I get stuck at the next step .. not sure what to multiply by, don't cancel the x to the fourth's out
 
  • #5
The second partial division and subtraction yielded a remainder. The process needed inclusion of the last both two terms in order to perform a sensible second subtraction; I needed to use all FIVE terms of the divisor, which is why the last two expanded form terms of the dividend were needed.

I have no easy way to typeset or express the numeric process in this forum. Let me just say, my final result after simplification was
-3x^2+(7/3)+(-8x^3 + 3x^2-(14/3)x+4)/(3x^4 -2x+1)

See if you can duplicate that! So many symbols and slightly lengthy, maybe I made an error.
 
  • #6
thats pretty much what I came up with , not sure though with it all being a remainder like that.. that's half the reason I thought my answer was wrong
 
  • #7
acuraintegra9 said:
thats pretty much what I came up with , not sure though with it all being a remainder like that.. that's half the reason I thought my answer was wrong

What course are you in? How does your textbook treat this topic? Did your teacher mention or give any example like the one you posted?

You could try checking my result using multiplying the result by the divisor; it should be found equivalent to the dividend.
 

FAQ: How Do You Solve Complex Polynomial Long Division Problems?

What is long division of polynomials?

Long division of polynomials is a method used to divide two polynomials, which are algebraic expressions with variables and coefficients. It is similar to long division of numbers, but instead of dividing numbers, we divide polynomials.

When do we use long division of polynomials?

We use long division of polynomials when we want to simplify or factor a polynomial expression, or when we want to find the quotient and remainder of dividing one polynomial by another.

How do we perform long division of polynomials?

To perform long division of polynomials, we follow these steps: 1) Arrange the polynomials in descending order of powers of the variable. 2) Divide the first term of the dividend (the polynomial being divided) by the first term of the divisor (the polynomial we are dividing by). This gives us the first term of the quotient. 3) Multiply the first term of the divisor by the first term of the quotient, and subtract the result from the first term of the dividend. This gives us the first term of the remainder. 4) Bring down the next term of the dividend and repeat the process until we have divided all terms of the dividend.

What are some common mistakes to avoid when doing long division of polynomials?

Some common mistakes to avoid when doing long division of polynomials include: 1) Forgetting to write a placeholder (a zero term) for any missing terms in the dividend. 2) Not bringing down the next term of the dividend after each iteration. 3) Making a mistake in the subtraction step, which can lead to incorrect remainder. 4) Using the wrong sign for the remainder. 5) Forgetting to add the remainder to the final quotient.

What should I do if I get a remainder when doing long division of polynomials?

If you get a remainder when doing long division of polynomials, you can either leave it as a remainder or write it as a fraction with the divisor as the denominator. The remainder can also be written in terms of the original problem, for example, if the original problem was to find the roots of a polynomial, then the remainder could be written as a factor of the polynomial.

Similar threads

How do you divide polynomials in your head "on sight"?
Replies
27
Views
4K
How Do You Solve Complex Absolute Value Inequalities?
Replies
4
Views
1K
Solving Polynomials: Factoring
Replies
12
Views
2K
How do I correctly solve this polynomial long division problem?
Replies
3
Views
2K
Solve the simultaneous equations involving x, y, and their squares
Replies
2
Views
786
Problem with a product of 2 remainders (polynomials)
Replies
4
Views
2K
How Can You Solve This Modulus Equation with Square Roots and Absolute Values?
Replies
1
Views
1K
Factoring Polynomials Using Synthetic Division
Replies
2
Views
1K
Long Division of cubic polynomial
Replies
3
Views
3K
Partial Fraction Question: HELP with Polynomial Long Division
Replies
4
Views
2K

Hot Threads

Recent Insights

Back
Top