State a definition of a polynomial in the x. Give an example of a monomial, a binomial and a trinomial. Thank you.
sum of terms each a constant times x to a power
2 x
2 x + 1
2 x^2 + x + 1
A polynomial in the variable x is an expression consisting of terms that are sums or differences of multiples of powers of x, with non-negative exponents.
Example of a monomial: 3x². It has only one term, where the coefficient is 3 and the variable is raised to the power of 2.
Example of a binomial: 4x + 2. It consists of two terms, 4x and 2, connected by a plus sign. The first term has the coefficient of 4 and is multiplied by x, while the second term has a coefficient of 2.
Example of a trinomial: 2x³ - 5x² + x. It consists of three terms, 2x³, -5x², and x, connected by minus signs. The first term has a coefficient of 2 and is raised to the power of 3, the second term has a coefficient of -5 and is raised to the power of 2, and the third term has a coefficient of 1.
To determine whether an expression is a monomial, binomial, or trinomial, count the number of terms in the expression. If there is only one term, it is a monomial. If there are two terms, it is a binomial. If there are three terms, it is a trinomial.