# what is the degree of the polynomial expression: x² + bx + c? Please explain your answer.

llltkl | College Teacher | (Level 3) Valedictorian

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The degree of the polynomial expression `x^2+bx+c` is 2.

The degree of a polynomial is the highest degree of its terms, when the polynomial is expressed in canonical form (i.e. as a linear combination of monomials). The degree of a term is the sum of the exponents of the variables that appear in it.

For example, the polynomial has three terms. (Notice, this polynomial can also be expressed as .) The first term has a degree of 5 (the sum of the powers 2 and 3), the second term has a degree of 1, and the last term has a degree of 0. Therefore, the polynomial has a degree of 5 which is the highest degree of any term.

Similarly, in the given expression the first term has a degree of 2, the second term has a degree of 1 and the last term has a degree of 0.

Therefore, the polynomial has a degree of 2 which is the highest degree of any term in the given expression.