Question

Which statement is true about the polynomial –10m4n3 + 8m2n6 + 3m4n3 – 2m2n6 – 6m2n6 after it has been fully simplified?

Answer 1

Answer:B

Step-by-step explanation:

Answer 2

The polynomial $-10m^4n^3 + 8m^2n^6 + 3m^4n^3-2m^2n^6-6m^2n^6$ consists of 5 monomials of form $C_1m^4n^3$ and $C_2m^2n^6.$

To simplify this polynomial, group terms that are of the same form:

1.

$-10m^4n^3+ 3m^4n^3=m^4n^3(-10+3)=-7m^4n^3.$

2.

$8m^2n^6-2m^2n^6-6m^2n^6=m^2n^6(8-6-2)=m^2n^6\cdot 0=0.$

Then the simpliest form of the polynomial $-10m^4n^3 + 8m^2n^6 + 3m^4n^3-2m^2n^6-6m^2n^6$ is $-7m^4n^3.$ You can see that only one monomial left and this monomial has a degree of 4+3=7.

Answer: correct option is B (a monomial with a degree of 7).