1. ## Naming Polynomials

I need to name this polynomial. y=(x+4)(x+1)(x-3)

Would it be a cubic polynomial because it's all multiplying, or would it be a linear?

Thanks

2. ## Re: Naming Polynomials

Its a cubic because once you expand it out (try it!) you get x cubed as the term with the highest order.

3. ## Re: Naming Polynomials

It's definitely cubic. It has exactly three roots.

4. ## Re: Naming Polynomials

Naming of polynomial in general is in accordance to the Order of the equation.
Now, what is order ?
Consider a polynomial in a single variable 'x'. Write the polynomial in its fully expanded form. Now search for the term that has the highest power on 'x' (like x squared or cubed etc.) Now that gives you the order of the polynomial. Now the naming is simple
Order Name
1 Linear
3 Cubic
and so on...

Hope that clears it !

5. ## Re: Naming Polynomials

Originally Posted by pratique21
Naming of polynomial in general is in accordance to the Order of the equation.
Now, what is order ?
Consider a polynomial in a single variable 'x'. Write the polynomial in its fully expanded form. Now search for the term that has the highest power on 'x' (like x squared or cubed etc.) Now that gives you the order of the polynomial. Now the naming is simple
Order Name
1 Linear
3 Cubic
and so on...

Hope that clears it !
I've always called an Order 4 polynomial a "Quartic".

6. ## Re: Naming Polynomials

to clarify: a general 4-th degree polynomial in x (or use your favorite variable name) is called a quartic (in x). a bi-quadratic is a quadratic in x2, which is a special kind of quartic.

to continue:

5-th degree polynomials are quintics, 6-th degree are sextics, and 7-th degree are septics. if you are dealing with even higher-level polynomials, although "latin" names do exists, it is usually easier to refer to them as "k-th degree polynomials" (and easier to remember, too).