What is the basic principle that can be used to simplify a polynomial? What is the relevance of the order of operations in simplifying a polynomial?
Combine the terms with the same exponent of the unknown (usually x). It does not matter in what order you do this.
If they mean to factor a polynomial instead of simplify it, that is much more difficult, especially if you have a cubic or higher order polynomial.
The basic principle to simplify a polynomial is to combine like terms. Like terms are terms that have the same variables raised to the same powers. To simplify a polynomial, you add or subtract the coefficients of the like terms.
The relevance of the order of operations, commonly known as PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction), is important in simplifying a polynomial because it helps ensure that the simplification is done correctly.
By following the order of operations, you perform the operations in the correct sequence. For example, if there are parentheses in a polynomial expression, you would first simplify what is inside the parentheses before combining like terms. Exponents are evaluated before any multiplication, division, addition, or subtraction. And finally, multiplication and division are done before addition and subtraction. Following this order ensures that you simplify the polynomial correctly and obtain the accurate result.