Question

A teacher asked 10 of his students to write a polynomial in one variable on paper. He asked them to handover the paper. The following were the answers given by the students:

𝟐𝒙 + 𝟑, $3x^2$ + 𝟕𝒙 + 𝟐, $4x^3+3x^2+2$, $x^3$ +$\sqrt{3x}$+ 𝟕, 𝟕𝒙 + $\sqrt{7}$ , $5x^3-7x+2$, $2x^2+3-\frac{5}{x}$, 𝟓𝒙 − $\frac{1}{2}$, $a{x}^3+b{x}^2+cx+d$, 𝒙 + $\frac{1}{x}$.

Based on the information above, answer the following questions:

(𝒊) How many of the above ten, are not polynomials?
(𝒊𝒊) How many of the above ten, are quadratic polynomials?

Answer 1

(𝒊) Non-polynomials exponents are not a whole number.
$x^3$ +$\sqrt{3x}$+ 𝟕,
$2x^2+3-\frac{5}{x}$,
𝒙 + $\frac{1}{x}$.


(𝒊𝒊) Quadratic polynomials are those whose highest degree is 2.
$3x^2+7x+2$