Degree of a Polynomial
The degree of the term with the highest exponent (or highest sum of the exponents) of the variable(s)
The degree of a polynomial is the highest power of the variable in the polynomial expression. For example, in the polynomial expression 4x^3 + 2x^2 + 7x + 9, the degree of the polynomial is 3 because the highest power of x is 3. The degree of a polynomial helps us to determine the behavior of the polynomial, such as its end behavior, as well as the number of roots it has.
It is important to note that the degree of a polynomial may be affected by any constants that are included in the expression. For example, if we add 5 to the expression 4x^3 + 2x^2 + 7x + 9 to get 4x^3 + 2x^2 + 7x + 14, the degree of the polynomial remains the same, because the highest power of x has not changed.
Knowing the degree of a polynomial can also help us with polynomial long division, factoring, and other algebraic manipulations. When dividing one polynomial by another, we must ensure that the degree of the divisor is lower than the degree of the dividend, so that we do not end up with a fraction that includes a polynomial with higher power than the original dividend.
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