Question

A polynomial of degree $5$ in $x$ has at most

• A. $5$ terms
• B. $4$ terms
• C. $6$ terms
• D. $10$ terms

Answer 1

Answer: (C)

$6$ terms

A polynomial of degree 5 is
$a_0{x}^5+a_1{x}^4+a_2{x}^3+a_3{x}^2+a_{4}x+a_5$, where $a_0,a_1,a_2,a_3,a_4,a_5$ are real constant.
Clearly maximum term in this polynomial are $6$ and also minimum term can be one $a_0{x}^5$.
Therefore, a polynomial of degree $5$ in $x$ has at most $6$ terms.