Question

Copy the expressions which are polynomials. Give reasons why the remaining are

Answer 1

Answer: a and c are polynomials, b is not.

Step-by-step explanation:

A polynomial p(x) is written as:

p(x) = aₙ*xⁿ + ... + a₂*x² + a₁*x¹ + a₀*x⁰

where x is the variable, and the numbers aₙ, aₙ₋₁, ..., a₁, a₀ are the coefficients of the polynomial, such that aₙ is the leading coefficient, and the value of n (always a natural number) is the degree of the polynomial.

Notice that the powers need to be always natural numbers.

Now, let's analyze the options:

a) 3*x - 2

We can rewrite this as:

3*x¹ - 2*x⁰

Then this is a polynomial.

b) p² + 1/p    (in this case the variable is p)

the second term can be written as:

1/p = p⁻¹

Then we have a term with a negative power of p, this means that this is not a polynomial.

c) 3*y² - 2*y/3 + 1

Same as in the first case, we can rewrite this as:

3*y² - (2/3)*y¹ + 1*y⁰

This is a polynomial.