Question

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

Answer 1

C is the correct choice here.

Answer 2

`30x^2 -26x-12` is a polynomial

Explanation:

Given : Two polynomials are
`5x- 6` and
`6x + 2`

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

Solution:

`\Rightarrow (5x- 6) * (6x + 2)`

`\Rightarrow5x(6x + 2) -6(6x+2)`

`\Rightarrow30x^2 + 10x -36x-12`

`\Rightarrow30x^2 -26x-12`

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.

`30x^2 -26x-12` is a polynomial