Question

Which statement justifies that x2 + 3x − 1 multiplied by 2x2 − 2x + 1 obeys the closure property of multiplication?

(A)The result 2x4 − 6x2 − 1 has a degree of 4.
(B)The result 2x4 − 6x2 − 1 is a trinomial.
(C) The result 2x4 + 4x3 − 7x2 + 5x − 1 has a degree of 4.
(D)The result 2x4 + 4x3 − 7x2 + 5x − 1 is a polynomial.

Answer 1

(x² + 3x - 1)(2x² - 2x + 1)

x²(2x² - 2x + 1) + 3x(2x² -2x + 1) -1(2x² - 2x + 1)
2x^4 - 2x³ + x² + 6x³ - 6x² + 3x - 2x² + 2x - 1
2x^4 - 2x³ + 6x³ + x² - 6x² - 2x² + 3x + 2x - 1
2x^4 + 4x³ - 7x² + 5x - 1

(D)The result 2x4 + 4x3 − 7x2 + 5x − 1 is a polynomial.

Answer 2

The statement that justify the product obeys the closure rule is the result 2x⁴ + 4x³ − 7x² + 5x − 1 is a polynomial

What is a polynomial?

A polynomial can have constants, variables and exponents, but never division by a variable.

Therefore, the statement that justify the product obeys the closure rule is as follows

(x² + 3x − 1)(2x² − 2x + 1 )

Hence,

(x² + 3x − 1)(2x² − 2x + 1 ) = 2x⁴ - 2x³ + x² + 6x³ - 6x² + 3x - 2x² + 2x + 1

2x⁴ - 2x³ + x² + 6x³ - 6x² + 3x - 2x² + 2x + 1 = 2x⁴ + 4x³ - 7x² + 5x  - 1

Therefore, 2x⁴ + 4x³ - 7x² + 5x  - 1 is a polynomial.

learn more on polynomials here: https://brainly.com/question/9855392

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