Question

Which statement justifies that 3x^2 − x − 5 multiplied by 2x^2 − x − 3 obeys the closure property of multiplication?

The result 6x^4 + x^2 + 15 has a degree of 4.
The result 6x^4 + x^2 + 15 is a trinomial.
The result 6x^4 − 5x^3 − 18x^2 + 8x + 15 is a polynomial.
The result 6x^4 − 5x^3 − 18x ^2 + 8x + 15 has a degree of 4.

Answer 1

(3x² - x - 5)(2x² - x - 3)

3x²(2x² - x - 3) -x(2x² - x - 3) - 5(2x² - x - 3)

6x⁴ - 3x³ - 9x² - 2x³ + x² + 3x - 10x² + 5x + 15
6x⁴ - 3x³ - 2x³ - 9x² + x² - 10x² + 3x + 5x + 15
6x⁴ - 5x³ - 18x² + 8x + 15

The result 6x^4 − 5x^3 − 18x^2 + 8x + 15 is a polynomial.