Question

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

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 $p\left(y\right)=y^2-y+1$

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

$p\left(0\right)=0^2-0+1=1$

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

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

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

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

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

$$\begin{gathered} p\left(2\right)=2^2-2+1 \\ =4-2+1 \\ =3 \end{gathered}$$

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

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