The polynomial which can be used to support the idea that the set of polynomials is closed under multiplication is: A. (5x - 1)(3x² + 4x).
What is a polynomial?
A polynomial can be defined as a mathematical expression which comprises intermediates (variables), constants, and whole number exponents with different numerical value, that are typically combined by using mathematical operations such as:
In Mathematics, a set is considered as closed under a multiplication operation, if the multiplication performed on two (2) elements of the set produces an element of the same set.
Note: The exponents of the variables are added when multiplying polynomials in accordance to the rules of exponents.
For option A, we have:
P = (5x - 1)(3x² + 4x)
P = 15x³ - 3x² + 20x² - 4x
P = 15x³ - 23x² - 4x.
For option B, we have:
P = (9x⁻³ - 5)(3x - 17)
P = 27x⁻² - 15x - 153x⁻³ + 85.
In conclusion, we can infer and logically deduce that the polynomial (5x - 1)(3x² + 4x) can be used to support the idea that the set of polynomials is closed under multiplication.
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