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Mathematics, 29.05.2020 07:01 asiamuhammad6

The set of polynomials is closed under the operation of addition.

A: Which equation illustrates this concept?

B: Which statement correctly explains this concept?

Select one answer for question A and one answer for question B.

A: (x+4)+(4xβˆ’5)=49

A: (2x2βˆ’3x+1)(2x+2)=4x3βˆ’2x2βˆ’4x+2

A: (xβˆ’3)+(3x+2)=βˆ’2xβˆ’5

A: (3xβˆ’4)βˆ’(2x+2)=xβˆ’6

B: The sum of the polynomials (2x2βˆ’3x+1) and (2x+2) is a polynomial, 2x2βˆ’x+3, which shows there is closure under addition.

A: (2x2βˆ’3x+1)+(2x+2)=2x2βˆ’x+3

B: The sum of the polynomials (x+4) and (4xβˆ’5) is not a polynomial, 49, which does not show there is closure under addition.

B: The sum of the polynomials (xβˆ’3) and (3x+2) is a polynomial, βˆ’2xβˆ’5, which shows there is closure under addition.

B: The product of the polynomials (2x2βˆ’3x+1) and (2x+2) is a polynomial, 4x3βˆ’2x2βˆ’4x+2, which shows closure under addition.

B: The difference of the polynomials (3xβˆ’4) and (2x+2) is a polynomial, xβˆ’6, which shows there is closure under addition.

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The set of polynomials is closed under the operation of addition.

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