Question

Which expressions are polynomials? select each correct answer

• x/5+2
• 35x^2
•7x^7-x^-5
•4x+square root x-1

Please help. Will reward for who knows the answers.

Answer 1

Expressions x/5+2 and 35x^2 are polynomials. 7x^7-x^-5 and 4x+square root x-1 are not, due to the presence of negative and fractional exponents respectively.

Step-by-step explanation:

To determine which expressions are polynomials, we must understand that a polynomial is an algebraic expression made up of terms that can include constants, coefficients, and variables raised to whole number exponents, combined using addition, subtraction, and multiplication (but not division by variables).

• x/5+2: This is a polynomial because the variable x is to the first power (a whole number), and the division by 5 is by a constant which is allowed.
• 35x^2: This is clearly a polynomial since it is a monomial with a variable raised to a whole number exponent.
• 7x^7-x^-5: This is not a polynomial because it contains a negative exponent, which is not allowed in polynomials.
• 4x+square root x-1: This is not a polynomial because the square root of x can be expressed as x^(1/2), which is not a whole number exponent.

The expressions that are polynomials are x/5+2 and 35x^2.

Answer 2

Note:
A polynomial of order n is of the form

`f(x)=a_(n)x^(n)+a_(n-1)x^(n-1) + \, ..., \, +a_(1)x+a_(0)`
where the a's are constants.

Consider the given expressions.
x/5 + 2 Not a polynomial
35x² It is a polynomial of order 2
7x⁷ - x⁵ It is a polynomial of order 7
4x + √(x-1) It is not a polynomial

Answer:
The polynomials are
35x²
7x⁷ - x⁵