Question

Classify the following as linear, quadratic and cubic polynomials: $x^2+x$.

Answer 1

Step 1: Understand the types of polynomial

Linear Polynomial – A polynomial whose degree is one is called a linear polynomial.

Example: $2x+1,\sqrt{2}y+1,2-u$.

Quadratic Polynomial – A polynomial of degree two is called a quadratic polynomial.

Example: $2x^2+5,5x^2+3x,x^2$ and $x^2+\frac{2}{5}x$

Cubic Polynomial – A polynomial of degree three is called a cubic polynomial.

Example: $4x^3,2x^3+1,5x^3+x^2,6x^3-6$

Step 2: Classify the given polynomial whether it is linear, quadratic, or cubic.

Given: $x^2+x$

We know that the highest power of the variable in a polynomial is called the degree of the polynomial.

Since the highest power of the variable in a polynomial is $2$.

Therefore the degree of the given polynomial is $2$.

Hence $x^2+x$ is a quadratic polynomial.