Thread: 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?

Please explain it to me..
Thanks

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

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

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
2 Quadratic
3 Cubic
4 Bi-quadratic
and so on...

Hope that clears it !

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
2 Quadratic
3 Cubic
4 Bi-quadratic
and so on...

Hope that clears it !

I've always called an Order 4 polynomial a "Quartic".

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).