Question

Explain why a constant polynomial such as $f\left(x\right)=4$ has degree 0 and a linear polynomial such as $f\left(x\right)=x+5$ has degree 1.

Short answer

It is interpreted that the degree of $f\left(x\right)=4$ is 0 and degree of $f\left(x\right)=x+5$ is 1.

Step-by-step solution

Step 1. Write down the given information.

The given polynomials are $f\left(x\right)=4 \text{and}f\left(x\right)=x+5$.

Step 2. Explanation.

The polynomial $f\left(x\right)=4 \text{and}f\left(x\right)=x+5$can be re-written as:

$\left.\begin{array}{l}f\left(x\right)=4{\left(x\right)}^0\\ f\left(x\right)={\left(x\right)}^1+5\end{array}\right)\mathrm{....}\left(1\right)$

From (1) it can be interpreted that the degree of $f\left(x\right)=4$is 0 and degree of $f\left(x\right)=x+5$is 1. Hence explained.

Step 3. Conclusion.

It is interpreted that the degree of $f\left(x\right)=4$ is 0 and degree of $f\left(x\right)=x+5$ is 1.