Question

which statement is true about the polynomial $5s^{6}t^{2} + 6st^{9} - 8s^{6}t^{2} - 6t^{7}$ after it has been fully simplified?

\bigcirc\\ it has 3 terms and a degree of 9.

\bigcirc\\ it has 3 terms and a degree of 10.

\bigcirc\\ it has 4 terms and a degree of 9.

\bigcirc\\ it has 4 terms and a degree of 10.

Explanation:

Step1: Combine like terms

$5s^6t^2 - 8s^6t^2 + 6st^9 - 6t^7 = (5-8)s^6t^2 + 6st^9 - 6t^7 = -3s^6t^2 + 6st^9 - 6t^7$

Step2: Count number of terms

The simplified polynomial has 3 distinct terms: $-3s^6t^2$, $6st^9$, $-6t^7$.

Step3: Calculate degree of each term

• Degree of $-3s^6t^2$: $6+2=8$
• Degree of $6st^9$: $1+9=10$
• Degree of $-6t^7$: $7$

Step4: Identify highest degree

The highest degree among the terms is 10.

Answer:

It has 3 terms and a degree of 10.