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.
I think it is B.

Answer 1

We have been given two polynomials $3x^2-2x -4 \text{ and } 2x^2+x-3$

Let us first multiply these polynomials.

$(3x^2 - 2x - 4)(2x^2 + x - 3)\\ \\ =3x^2(2x^2 + x - 3) -2x(2x^2 + x - 3)-4(2x^2 + x - 3)\\ \\ =6 x^4 - x^3 - 19 x^2 + 2 x + 12$

Now, we know that polynomials follows closure property of multiplication.

It means that when we multiply two polynomials, the result will be a polynomial.

Since, when we multiplied the given polynomials, we got $6 x^4 - x^3 - 19 x^2 + 2 x + 12$ which is a polynomial.

Therefore, the correct option is

The result $6 x^4 - x^3 - 19 x^2 + 2 x + 12$   is a polynomial.