is |x+9| a polynomial? Explain why or why not
as google's very first reference says:
Polynomials are expressions which only consist of variables and coefficients, using only the operations of: addition, subtraction, multiplication and natural exponents of variables. The absolute value operation is therefore not included in the scope of available operations for polynomials.
No, |x+9| is not a polynomial. A polynomial is an algebraic expression made up of variables, constants, and exponents, with addition, subtraction, and multiplication operations only. The absolute value function, denoted by ||, is not considered a polynomial because it involves a non-algebraic operation. In the expression |x+9|, the absolute value is taking the positive magnitude of the quantity (x+9), which is not a polynomial function.
To determine if |x+9| is a polynomial or not, let's first understand what a polynomial is. A polynomial is an algebraic expression consisting of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication, but not division or square roots.
In the case of |x+9|, we have an absolute value function. This function takes the argument inside the absolute value signs and returns a positive value, regardless of the sign of the argument. In this case, the argument is x+9.
Now, let's consider the argument x+9. This is a linear expression, as x is raised to the power of 1 (an exponent of 1). Linear expressions are a type of polynomial because they meet the criteria of a polynomial.
However, when we introduce the absolute value function, the overall expression |x+9| becomes non-polynomial. The absolute value function introduces a non-algebraic operation (taking the absolute value) into the expression, which means it doesn't meet the requirement of being a polynomial.
In conclusion, |x+9| is not a polynomial because it includes the absolute value function, which introduces a non-algebraic operation into the expression.