Question

Find $p\left(0\right),p\left(1\right)$ and $p(-2)$ for the following polynomial: $p\left(x\right)=10x-4x^2-3$

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 values

Given equation $p\left(x\right)=10x-4x^2-3$

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

$$\begin{gathered} p\left(0\right)=10\left(0\right)-4{\left(0\right)}^2-3 \\ =-3 \\ \therefore p\left(0\right)=-3 \end{gathered}$$

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

$$\begin{gathered} p\left(1\right)=10\left(1\right)-4{\left(1\right)}^2-3 \\ =10-4-3 \\ =3 \\ \therefore p\left(1\right)=3 \end{gathered}$$

Put the value $p(-2)$ in the given equation

$$\begin{gathered} p(-2)=10(-2)-4{(-2)}^2-3 \\ =-20-16-3 \\ =-39 \\ \therefore p(-2)=-39 \end{gathered}$$

Hence, $p\left(0\right)=-3$, $p\left(1\right)=3$ and $p(-2)=-39$