Question

Which statement justifies that 3x2 − 2x − 4 multiplied by 2x2 + x − 3 obeys the closure property of multiplication? The result 6x4 − 2x2 + 12 has a degree of 4. The result 6x4 − 2x2 + 12 is a trinomial. The result 6x4 − x3 − 19x2 + 2x + 12 is a polynomial. The result 6x4 − x3 − 19x2 + 2x + 12 has a degree of 4.

Answer 1

Answer: I believe the answer is C) The result 6x4 − x3 − 19x2 + 2x + 12 is a polynomial. !!!!!!!!

Answer 2

The result
`6x^4-x^3-19x^2+2x+12`.

is a polynomial.

Explanation:

The first polynomial is
`3x^2-2x-4`.

The second polynomial is
`2x^2+x-3`

The closure property of multiplication states that if we multiply two polynomials the result must be a polynomial.

The product of these two polynomials is :

`(3x^2-2x-4)(2x^2+x-3)=6x^4-x^3-19x^2+2x+12`.

We can see that the result is still a polynomial.