Which expressions are polynomials?

Option A: z + 1

Option B: 6 + w

Option D:

Solution:

Let us first define the polynomial.

A polynomial can have constants, variables, exponents and fractional coefficients.

A polynomial cannot have negative exponents, fractional exponents and never divided by a variable.

To find which expressions are polynomial:

Option A: z + 1

By the definition, z + 1 is a polynomial.

It is polynomial.

Option B: 6 + w

By the definition, 6 + w is a polynomial.

It is polynomial.

Option C:

Here, y have fractional exponent.

So, it is not a polynomial.

Option D:

By the definition, is a polynomial.

It is polynomial.

Hence z + 1, 6 +w and are polynomials.

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.