Question

Give five examples for linear polynomial, quadratic, cubic polynomial.

Answer 1

Step 1: Explaining Linear Polynomial:

A polynomial whose degree is one is said to be a linear polynomial.

Polynomials of the form $p\left(x\right):ax+b,a\ne 0$are linear polynomials.

Examples of a linear polynomial:-

$$\begin{gathered} \left(i\right)p\left(x\right):5x+7 \\ \left(ii\right)q\left(x\right):45x-90 \\ \left(iii\right)r\left(y\right):7y-8 \\ \left(iv\right)f\left(t\right):56t+67 \\ \left(v\right)k\left(z\right):8z+78 \end{gathered}$$

Step 2: Explaining Quadratic Polynomial:

A polynomial whose degree is two is said to be a quadratic polynomial.

Polynomials of the form $p\left(x\right):a{x}^2+bx+c,a\ne 0$are the quadratic polynomials.

Examples of a quadratic polynomial:-

$$\begin{gathered} \left(i\right)p\left(x\right):45x^2+7x-90 \\ \left(ii\right)q\left(x\right):4x^2+9x+6 \\ \left(iii\right)r\left(y\right):7y^2 \\ \left(iv\right)f\left(t\right):6t^2+7 \\ \left(v\right)k\left(z\right):8z^2+78z-67 \end{gathered}$$

Step 3 : Explaining Cubic Polynomial:

A polynomial whose degree is three is said to be a cubic polynomial.

Polynomials of the form $p\left(x\right):a{x}^3+b{x}^2+cx+d,a\ne 0$are cubic polynomials.

Examples of a cubic polynomial:-

$$\begin{gathered} \left(i\right)p\left(x\right):34x^3+5x^2+8x-9 \\ \left(ii\right)q\left(x\right):44x^3+9x^2+6x+2 \\ \left(iii\right)r\left(y\right):7y^3+56y^2 \\ \left(iv\right)f\left(t\right):6t^3+7 \\ \left(v\right)k\left(z\right):8z^3+78z^2-67z+7 \end{gathered}$$

Hence, A polynomial whose degree is one is said to be a linear polynomial, a polynomial whose degree is two is said to be a quadratic polynomial and a polynomial whose degree is three is said to be a cubic polynomial.

Hence the five examples for linear polynomial, quadratic, and cubic polynomial are given.