An algebraic expression with a degree of non-negative integer that has multiple terms made up of real numbers, variables and product of real numbers and variables is called _
A. divisor
B. factor
C. polynomial
D. root
The correct answer and explanation is:
The correct answer is C. polynomial.
A polynomial is an algebraic expression made up of terms that consist of real numbers, variables, and possibly the product of real numbers and variables raised to whole number exponents. The general form of a polynomial is a sum of terms, where each term is a product of a constant (called the coefficient) and a variable raised to a non-negative integer exponent. The degree of the polynomial is determined by the highest exponent of the variable in the expression.
Polynomials can have one or more terms. A polynomial with one term is called a monomial, with two terms a binomial, and with three terms a trinomial. For example, the expression 3×2+5x−73x^2 + 5x – 7 is a polynomial with three terms. Here, 3, 5, and -7 are the coefficients, and x2x^2, xx, and the constant term −7-7 represent the powers of the variable xx.
The degree of a polynomial is important because it helps in determining its behavior and how it will behave when graphed. For instance, a polynomial of degree 2, known as a quadratic, graphs as a parabola. Polynomials can be classified based on their degree as well. A polynomial of degree 1 is a linear polynomial, degree 2 is quadratic, degree 3 is cubic, and so on.
In contrast, the terms divisor, factor, and root do not directly relate to the definition of a polynomial. A divisor or factor refers to numbers or expressions that divide another expression without a remainder, and a root is the value of the variable that makes the polynomial equal to zero.