How to Write a Polynomial in Standard Form with Three Variables?

MHB
Thread starter bergausstein
Start date Oct 14, 2013
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Form Polynomials Standard

In summary, 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. The degree of a polynomial is the highest exponent of the variable in the polynomial, indicated by the exponent of the first term in standard form. The leading coefficient in standard form is the coefficient of the term with the highest degree. To convert a polynomial to standard form, the terms must be rearranged in descending order of degree and any missing terms are represented by a coefficient of 0. A polynomial can have more than one variable in standard form, with the terms arranged in descending order of the total degree, which is the sum of the exponents of each variable in each term.

Oct 14, 2013

bergausstein

how do you write a polynomial in three variables say x,y,z in standard form?

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Oct 14, 2013

alyafey22

Gold Member

MHB

The question is somehow vague , is this what you mean ?

\(\displaystyle P(x,y,z)= a_n (xyz)^n +a_{n-1}(xyz)^{n-1}+\cdots +a_1 xyz +a_0 \)

Related to How to Write a Polynomial in Standard Form with Three Variables?

What is the standard form of a polynomial?

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.

How do you determine the degree of a polynomial 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.

What is the leading coefficient in standard form?

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.

How do you convert a polynomial to standard form?

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.

Can a polynomial have more than one variable in standard form?

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).