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

$2x + 3$, $3x^2 + 7x + 2$, $4

Question

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

$2x + 3$, $3x^2 + 7x + 2$, $4x^3 + 3x^2 + 2$, $x^3 - \sqrt{3}x + 7$, $7x + \sqrt{7}$, $5x^3 - 7x + 2$, $2x^2 + 3 - \frac{5}{x}$, $5x - \frac{1}{2}$, $ax^3 + bx^2 + cx + d$, $x + \frac{1}{x}$

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

Accepted Answer

Step 1: (i) $2x^2 + 3 - \frac{5}{x}$, $x + \frac{1}{x}$, and $ax^3 + bx^2 + cx + d$ (constants not specified) are not polynomials. Total: 3
Step 2: (ii) Quadratic polynomials (degree 2): $3x^2 + 7x + 2$. Only 1 quadratic polynomial

Question

Solution