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Polynomials are mathematical expressions that are used to represent various functions, equations, and graphs. When we talk about the degree of a polynomial, we mean the highest or greatest power of a variable in the polynomial. It is important to note that the degree is only measured off the exponents on a variable.
An exponent is also known as an index or a power. These three terms refer to the same thing, and it is just a matter of preference as to which one you use. Generally, exponents, indices, or powers are going to be on variables. In contrast, you are not going to see an exponent on constant numbers. For instance, if there was a number to a power or a number with an index, you would go ahead and perform that operation.
To determine the degree of a polynomial, you need to figure out which power of the variable is the greatest. For instance, suppose you are given a polynomial like 3x² – 7x + 2x⁴. In that case, you would focus only on the powers of the variable and not the coefficients (the numbers in front of the variables). So the degree of this polynomial is 4 because the power of x in the term 2x⁴ is the greatest.
In conclusion, the degree of a polynomial is the highest power of a variable in the polynomial. It is essential to understand that the degree is only measured off the exponents on a variable. You can find the degree of a polynomial by figuring out which power of the variable is the greatest.
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