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Which statement shows how two polynomials 4x + 6 and 2x2 − 8x demonstrate the closure property when multiplied?

8x3 − 20x2 − 48x is a polynomial
8x3 − 20x2 + 48x may or may not be a polynomial
8x2 − 32x2 − 14x is a polynomial
8x3 − 32x2 + 14x may or may not be a polynomial

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JohnLayton
In order to multiply out two polynomials, we can us FOIL, which stands for First, Outer, Inner, Last. First, we multiply the first terms of the polynomials together, then the outer terms, etc. This gives us 8x^3 - 32x^2 + 12x^2 - 48x. By combining like terms, we can then get 8x^3 - 20x^2 - 48x. This term is a polynomial because it has more than 2 terms (it has 4). Therefore, the answer is A. 8x^3 - 20x^2 - 48x is a polynomial.

Hope this helps!

Answer:

[tex]8x^{3} -20x^{2} -48x[/tex] is a polynomial

Step-by-step explanation:

Given : polynomials [tex]4x+6[/tex] and[tex]2x^{2} -8x[/tex]

Solution:

[tex](4x+6)*(2x^{2} -8x)[/tex]

[tex]4x(2x^{2} -8x)+6(2x^{2} -8x)[/tex]

[tex]8x^{3} -32x^{2}+12x^{2} -48x[/tex]

[tex]8x^{3} -20x^{2} -48x[/tex]

Polynomial :An expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable.

Thus [tex]8x^{3} -20x^{2} -48x[/tex] is a polynomial

Hence option A is correct.




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