Question

ldentifica si las afirmaciones son verdaderas o falsas. Justifica la respuesta. El grado absoluto de un polinomio es el mayor exponente que tienen las

Equations and inequalities
ANSWERED
asked 2021-02-11
ldentifica si las afirmaciones son verdaderas o falsas. Justifica la respuesta.
El grado absoluto de un polinomio es el mayor exponente que tienen las variables del polinomio. El grado relativo de un polinomio respecto a una variable corresponde a la suma de los exponentes de dicha variable. En un polinomio dos o más términos son semejantes cuando su parte literal es la misma. El opuesto de un polinomio se obtiene al cambiar los signos y determinar los valores recíprocos de los coeficientes. El término independiente de un polinomio es el término de grado cero en el polinomio.

Answers (1)

2021-02-12
This statement is false. The absolute degree of a polynomial is the largest sum of the exponents of each term in the polynomial. For example, the absolute degree of the polynomial \(\displaystyle{x}^{{{2}}}{y}^{{{2}}}+{x}{y}^{{{2}}}+{x}{\left\lbrace{2}\right\rbrace}{x}\) is 4 since the sum of the exponents for the first term is 2+2=4, the sum of the exponents for the second term is 1+2=3, and the third term has a sum of 2. Since 4 is the largest sum, the absolute degree of the polynomial is 4.
This statement is false. The relative degree of a polynomial with respect to a variable is the largest exponent of that variable. For example, the relative degree with respect to xx of the polynomial \(\displaystyle{x}^{{{3}}}{y}+{x}^{{{2}}}{y}^{{{2}}}+{x}\) is 3 since the largest exponent for the variable of xx is 3.
This statement is true. If the terms have the same variables and exponents, then the terms are similar.
This statement is false. The opposite of a polynomial is obtained by only changing the signs of the coefficients. You do not find the reciprocals of the coefficients.
This statement is true. The independent term, or constant term, is the term that has a literal part that is degree zero. For example, the independent term of the polynomial \(\displaystyle{x}^{{{2}}}+{x}+{4}{x}\) is 4 because the term 4 has a degree of 0 since \(\displaystyle{4}={4}{x}^{{{0}}}\).
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