How do I divide polynomials? (x^3-15x-7)/(x^2-3x-3)

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In summary, dividing polynomials involves using the long division method to simplify the expression. First, arrange the polynomials in descending order and make sure to include any missing terms with a coefficient of zero. Then, divide the first term of the dividend by the first term of the divisor to get the first term of the quotient. Multiply this term by the entire divisor and subtract it from the dividend. This will give you the remainder, which is placed on top of the next term of the dividend. Repeat this process until there are no more terms left in the dividend and the remainder is less than the divisor. The resulting quotient is the answer to the division of the polynomials. It is important to check for any extraneous solutions and simplify the final
  • #1
Learning
Ok, I have been trying to divide this polynomial.

(x^3-15x-7)/(x^2-3x-3)

After I factor the first part I get stuck. This is last problem on my homework and is due in less than an hour. Please some one help me out. Thanks
 
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  • #2
_x__+3_________
(x^3-15x-7)|x^2-3x-3
-
x^3-3x^2-3x
------------
3x^2-12x-7
-
3x^2-9x-9
------------
-3x+2

so the answer is (x+3)*(x^2-3x-3)-3x+2=x^3-15x-7

im sorry for my long division it's just the lack of other way of doing it.
 
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  • #3


To divide polynomials, you can use the long division method or the synthetic division method. Both methods involve dividing the highest degree term of the dividend (numerator) by the highest degree term of the divisor (denominator).

Let's start with the long division method. First, arrange the terms in descending order of degree:

(x^3-15x-7)/(x^2-3x-3)

Next, divide the first term of the dividend (x^3) by the first term of the divisor (x^2). This gives you x as the first term of the quotient. Then, multiply this term by the entire divisor (x^2-3x-3) and write the result below the dividend, like this:

x
_____________________
x^2-3x-3 | x^3-15x-7

Next, subtract the result from the dividend and bring down the next term (in this case, -15x):

x
_____________________
x^2-3x-3 | x^3-15x-7
-(x^3-3x^2-3x)
______________
-12x-7

Repeat this process until you've gone through all the terms in the dividend. In this case, you will get a remainder of -12x-7. So the final quotient will be x with a remainder of -12x-7 over the divisor:

x - (12x+7)/(x^2-3x-3)

Alternatively, you can use the synthetic division method. This method is a quicker way to divide polynomials when the divisor is in the form of (x-a). In this case, the divisor is (x^2-3x-3), so we need to factor it first. You can use the quadratic formula or other methods to factor it into (x-3)(x+1).

(x^3-15x-7)/(x^2-3x-3)
= (x^3-15x-7)/(x-3)(x+1)

Now, set up the synthetic division table by writing the coefficients of the dividend (x^3-15x-7) in the first row and the factors of the divisor (x-3)(x+1) in the second row:

3 | 1 -15 -7
-1 | 1 -3 3

Next, bring down the first
 

1. How do you divide polynomials?

Dividing polynomials involves using long division or synthetic division, similar to dividing regular numbers. You divide the terms of the polynomials by their highest degree terms, and then simplify the result.

2. What is the difference between long division and synthetic division?

Long division is the traditional method of dividing polynomials, where you write out the terms and divide them step by step. Synthetic division is a more abbreviated method that is used when dividing by a linear expression (a polynomial with only one term). It involves using only the coefficients of the terms and simplifying them along the way.

3. Can you divide polynomials with different degrees?

Yes, you can divide polynomials with different degrees. However, the result will not always be a polynomial. If the degree of the divisor (the polynomial you are dividing by) is larger than the degree of the dividend (the polynomial being divided), the result will be a fraction with a polynomial in the numerator and the divisor in the denominator.

4. What is the remainder when dividing polynomials?

The remainder in polynomial division is the term that is left over after the division is complete. It is always a polynomial with a degree that is less than the divisor. The remainder can also be written as a fraction with the polynomial in the numerator and the divisor in the denominator.

5. Can you use polynomial division to solve real-world problems?

Yes, polynomial division can be used to solve real-world problems, such as determining the amount of a substance present in a mixture or calculating the number of items that can be produced from a given amount of material. It is a useful tool in many areas of science and engineering.

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