Q.78 - Intermediate Algebra

Question

Using your own words, explain the difference between a polynomial with five terms and a polynomial with a degree of $5$.

Step-by-Step Solution

Answer

A polynomial of degree 5 is one whose highest degree is 5 and a polynomial with five terms can have 5 terms and NOT be of degree 5.

Step 1. Given Information

In the given question, using our own words, we have to explain the difference between a polynomial with five terms and a polynomial with a degree of $5$.

Step 2. A definition of a polynomial with five terms and a polynomial with a degree of 5 .

• A polynomial of degree $5$ is one whose highest degree is $5$.
• A polynomial with five terms can have  terms and NOT be of degree $5$.

Step 3. The difference between a polynomial with five terms and a polynomial with a degree of 5 .

A polynomial of degree 5 is one whose highest degree is 5.  For example, 

$f\left(x\right) = a_5{x}^5 +a_4{x}^4+a_3{x}^3+a_2{x}^2+a_{1}x+ a_0$

with $a_5\ne 0$.  Any of the other $a_i$ can be zero, but not $a_5$.

On the other hand, a polynomial can have 5 terms and NOT be of degree 5.  For example,

$h\left(x\right) = 2x^9 + 6x^7 + 4x^4 - 8x + 2$

A polynomial of degree $n$ can have at most $n+1$ terms.