The statement that justifies why (2x² + x − 3) × (x² − 3x - 2) obeys the closure property of multiplication is: a. The result 2x⁴ - 5x³ - 10x² + 7x + 6 is a polynomial.
What is the Closure Property of Multiplication?
The closure property of multiplication states that when we multiply two rational expressions or numbers together, the result we get would be a rational number or expression also.
For example, if we multiply two rational numbers, m and n together to get mn, mn will also be a rational number.
In the same vein, if we multiply two polynomials together, the result will be a polynomial as well.
Thus, we have:
(2x² + x − 3)(x² − 3x - 2)
Apply the distribution property to remove the brackets
2x²(x² − 3x - 2) + x(x² − 3x - 2) -3(x² − 3x - 2)
2x⁴ - 6x³ - 4x² + x³ - 3x² - 2x - 3x² + 9x + 6
Combine like term
2x⁴ - 5x³ - 10x² + 7x + 6
Thus, 2x⁴ - 5x³ - 10x² + 7x + 6, is a polynomial. This obeys the closure property of multiplication.
Therefore, the answer is: a. The result 2x⁴ - 5x³ - 10x² + 7x + 6 is a polynomial.
Learn more about the closure property of multiplication on:
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