Determine how many linear factors and zeros each polynomial function has. P(x)=x^{40} + x^{39}

Emeli Hagan 2021-02-27 Answered
Determine how many linear factors and zeros each polynomial function has.
P(x)=x40+x39
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

mhalmantus
Answered 2021-02-28 Author has 106 answers
Number of zeros theorem:
If multiple zeros are counted individually, the polynomial function P(x) with degree n(n>0)
has exactly n zeros among the complex numbers.
The Polynomial Factorization Theorem:
If n>0 and P(x) is an nth-degree polynomial function, then P(x) has exactly n linear factors:
P(x)=an(xc1)(Xc2)(Xc3).....(xCn)
Where c1,c2,c3,....,cn are numbers and an, is the leading coefficient of P(x).
Finding zeros:
Given:
P(x)=x40+x39
According to the Number of zeros theorem, the polynomial function P(x) has n zeros.
Where n is the degree of the polynomial function
Here n=40
Hence the zeros of the polynomial function P(x)=x40+x39 is 40
Finding linear factors:
Given:
P(x)=x40+x39
According to The Polynomial Factorization Theorem, the polynomial function P(x) has n linear factors.
Where n is the degree of the polynomial function
Here n=40
Hence the linear factors of the polynomial function P(x)=x40+x39 is 40
Final statement:
The number of linear factors of the polynomial function P(x)=x40+x39 are 40.
The zeros of the polynomial function P(x)=x40+x39 are 40.
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

New questions