Question

Which statement is true about the polynomial 5s6t2 + 6st9 – 8s6t2 – 6t7 after it has been fully simplified? It has 3 terms and a degree of 9. It has 3 terms and a degree of 10. It has 4 terms and a degree of 9. It has 4 terms and a degree of 10.

Answer 1

Answer: The polynomial has 3 terms and a degree of 10.

Step-by-step explanation:

The given polynomial: $5s^6t^2 + 6st^9 - 8s^6t^2 - 6t^7$

Here, two terms $5s^6t^2$ and $8s^6t^2$ have same power for s and t i.e. they are like terms.

Combine like terms , we get

$6st^9 - 3s^6t^2 - 6t^7.$ i.e. there are 3 terms.

Degree of $6st^9$  is 1+9=10;

Degree of $- 3s^6t^2$ is 6+2=8;

Degree of  $- 6t^7$  is 7.

Since degree of the polynomial = highest degree i.e. 10

Hence, the polynomial has 3 terms and a degree of 10.

Answer 2

The statement which is true about the polynomial 5s⁶t² + 6st⁹ – 8s⁶t² – 6t⁷ is; It has 4 terms and a degree of 10.

Discussion:

By counting the number of terms in the polynomial;

• We can conclude that the polynomial has 4 terms and hence can be called a tetranomial.

Additionally, the degree of the polynomial is 10.

This is from the term with the highest degree which is; 6st⁹; where s has degree 1 and t has degree 9; total of which is; 10.

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