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In Exercises 27 - 48, find all of the zeros of the polynomial then completely factor it over the real numbers and completely factor it over the complex numbers
Today: algebra of polynomials, factor theorem, statement of the fundamental theorem of algebra Next time: synthetic division, other tools for finding roots,
We have the: Remainder Theorem: When a polynomial P(x) is divided by x - r, the remainder is P(r) Example: If p(x) = x4 + x3 - x2 - 2x + 3 Since p(2) = (2)
Putting the Factor Theorem and the Fundamental Theorem of Algebra together says that if p is a polynomial of degree n, then there exists ?1 ? C such that p(z)=(
Theorem For the rational number p q to be a zero, p must be a factor of a0 If P(x) is a polynomial of degree n > 0, then there exist complex numbers
A complex number is the sum of a real number and an imaginary number Complex Number z , then the Factor Theorem guarantees that f can be factored as
Over the complex numbers, every polynomial has a root and so every polynomial will factorise into linear factors: Theorem 0 4 (Fundamental Theorem of
The Division Algorithm, Remainder Theorem, and Factor Theorem all remain true for polynomials with complex coefficients Complex number were discovered in
27 août 2010 · You need to know about adding and multiplying complex numbers Page 2 Clearing a variable Many Mathematica examples will use the variable z