Question 173737: 4x6-x3_5 How do i know if this is a polynomial
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! A polynomial is a mathematical expression consisting of a sum of terms, each term including a variable or variables raised to a power and multiplied by a coefficient.
So  has three terms, and each term has the variable  raised to a power. The first term has raised to the 6th power, the second term has raised to the 3rd power, and the last term actually has the variable in it raised to the 0 power. By convention, you don't bother to write the variable raised to the 0 power because any number raised to the 0 power equals 1 by definition (although it would be perfectly proper to write  ). Even though there are minus signs between the first and second terms and between the second and third terms, you are actually summing the terms because you are adding terms with negative coefficients, in other words:  . Also, just because you don't see a coefficient, that doesn't mean there isn't one. If you don't see a coefficient, then the coefficient is 1. Furthermore, the coefficient includes the sign preceeding the term.
Most definitions of polynomial require that there be at least two terms, with a one term expression being called a monomial.
And that's how you know.
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