Question

Find $p\left(0\right),p\left(1\right)$ and $p\left(2\right)$ for the following polynomial: $p\left(x\right)=(x-1)(x+1)$

Answer 1

Step 1. Define a Polynomial

A polynomial is an algebraic expression in which the exponent on any variable is a whole number. Polynomial’s degree is the highest or the greatest power of a variable in a polynomial equation. The degree indicates the highest exponential power in the polynomial.

Step 2. Find the required values

Given equation $p\left(x\right)=(x-1)(x+1)$

Put the value $p\left(0\right)$ in the given equation

$p\left(0\right)=(0-1)(0+1)=-1$

$\therefore p\left(0\right)=-1$

Put the value $p\left(1\right)$ in the given equation

$$\begin{gathered} p\left(1\right)=(1-1)(1+1) \\ =0\times 2 \\ =0 \\ \therefore p\left(1\right)=0 \end{gathered}$$

Put the value $p\left(2\right)$ in the given equation

$$\begin{gathered} p\left(2\right)=(2-1)(2+1) \\ =1\times 3 \\ =3 \end{gathered}$$

$\therefore p\left(2\right)=3$

Hence, $p\left(0\right)=-1$, $p\left(1\right)=0$ and $p\left(2\right)=3$