Quartic polynomials?

Question

so... if any 3 linear factors are expanded they will always become a cubic polynomial (a polynomial with a degree of 3):

eg: x(x+2)(x-3) = x*3-x*2-6x

OR (x-1)(x+5)(x+2) = x*3+6x*2+3x-10

what does a factorised quartic polynomial look like? i know what a expanded on is: a polynomial with a degree of 4....but im not sure of a factorised one.

Answer 1

A quartic polynomials will have 4 roots and thus it must have 4 linear factor like

(x + 1)(x + 2)(x + 3)(x + 4) and it will exactly give back the polynomials you tried to factorize...Just remember that each and every polynomials will have the same number of roots/factors according to their highest degree of the polynomials..Hope that helps♣\

PEACE

Answer 2

It's the same as a cubic except there are 4 linear factors. For example:

(x + 1)(x + 2)(x + 3)(x + 4) = ...

or

x(x + 1)(x + 2)(x + 3) = ...

Answer 3

example x^4-1

=(x^2-1)(x^2+1)

=(x-1)(x+1)(x^2+1)