Question

Find $p\left(0\right),p\left(1\right)$ and $p\left(2\right)$ for the following polynomial: $p\left(t\right)=2+t+2t^2-t^3$

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 value

Given equation $p\left(t\right)=2+t+2t^2-t^3$

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

$p\left(0\right)=2+\left(0\right)+2.\left(0^2\right)-0^3=2$

$\therefore p\left(0\right)=2$

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

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

$\therefore p\left(1\right)=4$

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

$$\begin{gathered} p\left(2\right)=2+2+2.{\left(2\right)}^2-2^3 \\ =2+2+8-8 \\ =4 \end{gathered}$$

$\therefore p\left(2\right)=4$

Hence, $p\left(0\right)=2$, $p\left(1\right)=4$ and $p\left(2\right)=4$