A polynomial is a mathematical expression consisting of variables (such as x and y) and constants (such as numbers) combined using addition, subtraction, and multiplication, but not division. It can have multiple terms, with each term containing a variable raised to a non-negative integer power.
To solve a polynomial equation, you need to first simplify the expression by combining like terms and using the distributive property. Then, set the expression equal to zero and use algebraic techniques such as factoring, the quadratic formula, or synthetic division to find the values of the variable that make the equation true.
The degree of a polynomial is the highest exponent of the variable in the expression. For example, if the expression is 2x^3 + 5x^2 + 3x + 1, the degree is 3 because x is raised to the power of 3 in the first term.
No, a polynomial cannot have negative exponents. In a polynomial, the exponents must be non-negative integers, meaning they can only be 0, 1, 2, 3, and so on. If a polynomial has a term with a negative exponent, it is not considered a polynomial.
A monomial is a polynomial with only one term, while a polynomial can have multiple terms. For example, 3x^2 is a monomial, while 3x^2 + 5x + 2 is a polynomial with three terms.