Question

which term can be added to the polynomial expression $5x^{7}-6x^{6}+4x^{4}-4x^{2}$ to make it into a 10th degree polynomial?
10
$5x^{3}$
$5x^{7}$
$x^{10}$

Explanation:

Step1: Recall polynomial degree concept

The degree of a polynomial is the highest power of the variable in the polynomial.

Step2: Analyze given polynomial

The given polynomial $5x^{7}-6x^{6}+4x^{4}-4x^{2}$ has the highest - power term $5x^{7}$, so its degree is 7.

Step3: Determine required term

To make it a 10 - th degree polynomial, we need to add a term with the power of the variable equal to 10.

Answer:

D. $x^{10}$