Question

Write a polynomial of degree 5 that has three terms.

Short answer

The polynomial of degree 5 having three terms is$x^5+2x^4+3x^3$ .

Step-by-step solution

Step 1. Write down the given information.

The given polynomial has degree 5.

Step 2. Calculation.

The standard polynomial of degree 5 having three terms is written as:$a_0{x}^n+a_1{x}^{n-1}+a_2{x}^{n-2}+a_3{x}^{n-3}+a_4{x}^{n-4}$ in order of decreasing order of degree where any two terms can be equated to zero.

Now for the polynomial to be of three terms and degree 5, we have following one possible situation.

$\begin{array}{l}\{a_0,a_1,a_2\}\ne 0\text{and}n=5\\ \{a_0,a_1,a_2\}\in R\text{\hspace{0.17em}and}n\in Z^{+}\end{array}$

Therefore, one possible case for polynomial of degree 5 having three terms is written as:$x^5+2x^4+3x^3$

Step 3. Conclusion.

The polynomial of degree 5 having three terms is $x^5+2x^4+3x^3$.