Answer:
C) The result 6x⁴ − x³ − 19x² + 2x + 12 is a polynomial.
Step-by-step explanation:
We have been given two polynomials [tex]3x^2-2x -4 \text{ and } 2x^2+x-3[/tex].
Let us first multiply these polynomials.
[tex](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[/tex]
Now, we know that polynomials follows closure property of multiplication, we can come to the conclusion that when we multiply the two polynomials, the result will be a polynomial.
Since, when we multiplied the given polynomials, we got [tex]6 x^4 - x^3 - 19 x^2 + 2 x + 12[/tex] which is a polynomial.
Therefore, the correct option is:
C) The result 6x⁴ − x³ − 19x² + 2x + 12 is a polynomial.
