Question

Which statement is true about the polynomial 5s^6t^2 + 6st^2 - 8s^6t^2 - 6t^7 after it has been fully simplified?

Answer 1

Given:

The polynomial is

$5s^6t^2+6st^2-8s^6t^2-6t^7$

To find:

The correct statement about the given polynomial.

Solution:

We have,

$5s^6t^2+6st^9-8s^6t^2-6t^7$

On combining like term, we get

$=(5s^6t^2-8s^6t^2)+6st^9-6t^7$

$=-3s^6t^2+6st^9-6t^7$

Here, the terms are $-3s^6t^2, 6st^9, 6t^7$. So, the number of terms is 3.

The degree of the polynomial is the highest power of the variable or the product of the variables.

Powers of $-3s^6t^2, 6st^9, 6t^7$ terms are 6+2=8, 1+9=10, 7.

Since the highest power of the product of the variable is 10, therefore, the degree of the polynomial is 10.

Hence the correct option is b.