Respuesta :
Answer:
They all are polynomials.
Step-by-step explanation:
Given : Following expression
1) [tex]x^2+5x^{15}[/tex]
2) [tex]-x^2+5x[/tex]
3) [tex]6x^2+5x[/tex]
4) [tex]-7x^2+53x[/tex]
The following all are polynomials because polynomials are:
An expression consisting of variables and coefficients or expression more than two algebraic terms and the terms that contain different powers of the same variable(s) involve operations addition , subtraction, multiplication and non-negative integer exponent of variables.
So when we see to these functions they all are a mixture of a polynomial.
We know that a polynomial is a mathematical expression consisting of a sum of terms, each term including a variable or variables raised to a power (usually positive whole number) and multiplied by a coefficient.
All the given expressions are polynomials.
[tex]x^{2} +5x^{15}, \:-x^{2} +5x,\: 6x^{2} +5x, \:-7x^{2}+53x[/tex]
The simplest polynomials have one variable.
A one-variable polynomial of degree n has the following form:
[tex]a_{n}x^{n} +a_{n-1}x^{n-1} +a_{n-2}x^{n-2} +.....+ a_{2}x^{2}+a_{1}x^{1} +a[/tex]
Where, the a's represent the coefficients and x represents the variable.
Now, consider the given options:
Given expression:
1) [tex]x^{2} +5x^{15}[/tex] is a mathematical expression consisting of a sum of terms, each term including a variable or variables raised to a power and multiplied by a coefficient. Also, the exponent of the variable x is a whole number.Therefore, [tex]x^{2} +5x^{15}[/tex] is a polynomial
2) [tex]-x^{2} +5x[/tex] is a mathematical expression consisting of a sum of terms, each term including a variable or variables raised to a power and multiplied by a coefficient. Also, the exponent of the variable x is a whole number.Therefore, [tex]-x^{2} +5x[/tex] is a polynomial
3) [tex]6x^{2} +5x[/tex] is a mathematical expression consisting of a sum of terms, each term including a variable or variables raised to a power and multiplied by a coefficient. Also, the exponent of the variable x is a whole number.Therefore, [tex]6x^{2} +5x[/tex] is a polynomial
4) [tex]-7x^{2}+53x[/tex] is a mathematical expression consisting of a sum of terms, each term including a variable or variables raised to a power and multiplied by a coefficient. Also, the exponent of the variable x is a whole number.Therefore, [tex]-7x^{2}+53x[/tex] is a polynomial.
Hence, all the expressions are polynomial.
For more information:
https://brainly.com/question/12491437
