Which statement shows how two polynomials 5x − 6 and 6x + 2 demonstrate the closure property when multiplied?
A: 30x2 − 26x − 12 may or may not be a polynomial
B:30x2 − 11x − 12 may or may not be a polynomial
C:30x2 − 26x − 12 is a polynomial
D:30x2 − 11x − 12 is a polynomial

Respuesta :

C is the correct choice here.

Answer:

[tex]30x^2 -26x-12[/tex]   is a polynomial

Step-by-step explanation:

Given : Two polynomials are [tex]5x- 6[/tex] and [tex]6x + 2[/tex]

To Find: Which statement shows how two polynomials demonstrate the closure property when multiplied?

Solution:

[tex]\Rightarrow (5x- 6) \times (6x + 2)[/tex]

[tex]\Rightarrow5x(6x + 2) -6(6x+2)[/tex]

[tex]\Rightarrow30x^2 + 10x -36x-12[/tex]

[tex]\Rightarrow30x^2 -26x-12[/tex]

Definition of Polynomial :  A mathematical expression of one or more algebraic terms each of which consists of a constant multiplied by one or more variables raised to a non negative integral power is called a polynomial.

So, Option C is true.

[tex]30x^2 -26x-12[/tex]  is a polynomial