tell me about polynomials and degree
Answers
the highest power on the variable or on the number will be the degree of the polynomial
Answer:
The degree of a polynomial is the highest degree of its monomials (individual terms) with non-zero coefficients. The degree of a term is the sum of the exponents of the variables that appear in it, and thus is a non-negative integer. The term order has been used as a synonym of degree but, nowadays, may refer to several other concepts (see order of a polynomial (disambiguation)). For example, the polynomial { 7x^{2}y^{3}+4x-9,} {7x^{2}y^{3}+4x-9,} which can also be expressed as {7x^{2}y^{3}+4x^{1}y^{0}-9x^{0}y^{0},} {7x^{2}y^{3}+4x^{1}y^{0}-9x^{0}y^{0},} has three terms. 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.
To determine the degree of a polynomial that is not in standard form (for example: {(x+1)^{2}-(x-1)^{2}} (x+1)^{2}-(x-1)^{2}), one has to put it first in standard form by expanding the products (by distributivity) and combining the like terms; for example {(x+1)^{2}-(x-1)^{2}=4x} (x+1)^{2}-(x-1)^{2}=4x is of degree 1, even though each summand has degree 2. However, this is not needed when the polynomial is expressed as a product of polynomials in standard form, because the degree of a product is the sum of the degrees of the factors.
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