Polynomials: Definitions, Types, and Theorems

The general form of a polynomial is a_n x^n + a_(n-1) x^(n-1) +...+ a_1 x + a_0, where 'n' represents the degree of the polynomial, which is the highest power of the variable.

A monomial is a polynomial with only one term, while a binomial is a polynomial with two terms.

The Fundamental Theorem of Algebra states that every non-constant polynomial has at least one complex zero.

<p>The number of zeroes of a polynomial is equal to its degree, counting multiplicities.</p> Signup and view all the answers

<p>The Remainder Theorem states that if a polynomial <code>f(x)</code> is divided by <code>x - a</code>, the remainder is <code>f(a)</code>. It can be used to find the value of a polynomial at a specific point.</p> Signup and view all the answers

<p>The Factor Theorem states that if <code>a</code> is a zero of a polynomial <code>f(x)</code>, then <code>x - a</code> is a factor of <code>f(x)</code>.</p> Signup and view all the answers

<p>A constant polynomial is a polynomial with only a constant term, whereas a zero polynomial is a polynomial with all coefficients equal to zero.</p> Signup and view all the answers

<p>A trinomial is a polynomial with three terms, whereas a binomial is a polynomial with two terms.</p> Signup and view all the answers

<p>The Fundamental Theorem of Algebra guarantees that every non-constant polynomial has at least one complex zero, which is related to the number of zeroes of a polynomial being equal to its degree.</p> Signup and view all the answers