Integral Zero Theorem

Integral Zero Theorem

Hey guys this is Jose and today I will be spamming this blog with pictures and examples!

When factoring a polynomial p(x), it is helpful to know which integer values of a to try when determining if p(a) = 0. Consider the polynomial p(x) = x^3 - 7a^2 +14x - 8. If x =a satisfies p(a)  = 0, then a^3 - 7a^2 +14a- 8 =0 or a^3  -7a ^ 2+ 14a - 8 = 0. or a^3 - 7a^2 + 14a = 8. Factoring out the common factor on the left side  of the equation gives the product a(a^2 - 7a +14) = 8. Then, the possible integer  values for the factors in the product on the left side are factors of 8. +/-1,+/-2,+/-4 and +-8.


The relationship between the factors of a polynomial and the constant term of the polynomial is stated in the Integral Zero Theorem.

*NOTE*

Integral Zero Theorem States that if x - a is a factor of a polynomial function p(x) with integral coefficients, then a is a factor of the constant term of p(x)

Example: (1)

                  (2)      

                    (3)           

And here is a picture  for those who couldn't comprehend this .

                                                   Mr. Piateck          

Student 

We also did some  High-Degree Polynomials tuturu!!!!

*VERY IMPORTANT (PROVINCIAL EXAM) TYPE OF QUESTION*

*An Intermodal container that has the shape of a rectangular prism has a volume, in cubic feet, represented by the polynomial function  V(x) = x^3 + 7x^2 - 28x +20, where x is a positive real number, What are factors that represent possible dimensions, terms of x, of the container?*

This Is The End of The Blog now take a break and go eat.