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bergausstein
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how do you write a polynomial in three variables say x,y,z in standard form?
The standard form of a polynomial is when the terms are arranged in descending order of degree, and the coefficient of each term is written in front of it. For example, 3x^2 + 5x + 2 is in standard form.
The degree of a polynomial is the highest exponent of the variable in the polynomial. In standard form, the degree is indicated by the exponent of the first term. For example, in the polynomial 3x^2 + 5x + 2, the degree is 2.
The leading coefficient in standard form is the coefficient of the term with the highest degree. In the polynomial 3x^2 + 5x + 2, the leading coefficient is 3.
To convert a polynomial to standard form, you need to rearrange the terms in descending order of degree and write the coefficient of each term in front of it. If there is a missing term, it is represented by a coefficient of 0. For example, the polynomial x^3 + 2x^2 - 5 can be written in standard form as x^3 + 2x^2 + 0x - 5.
Yes, a polynomial can have more than one variable in standard form. In this case, the terms are arranged in descending order of the total degree, which is the sum of the exponents of each variable in each term. For example, the polynomial 2x^2y + 3xy^2 + 4y^3 is in standard form because the total degree of the first term is 3 (2 + 1) and the total degree of the second term is also 3 (1 + 2).