1. Polynomials are not closed under which of the following operations?

Question

A. addition
B. multiplication
C. division
D. Subtraction
2. The difference of two polynomials must always result in a _____.
A. Polynomial
B. Monomial
C. Binomial
D. Trinomial
3. Can a binomial be multiplied by a monomial such that the product is a monomial? If so, give an example.
A. Yes. 2(2x+y)=4x+2y
B. Yes. 0(2x+y)=0
C. No. A binomial can never be multiplied by a monomial such that the product is a monomial.
D. Yes. 1(2x+y)=2x+y
4. Can two polynomials be subtracted such that the difference is a binomial? If so, give an example. If not, explain.
A. No. When two polynomials are added from each other, they will always equal a polynomial.
B. No. When two polynomials are subtracted from each other, they always equal a monomial.
C. Yes. (3b^2−3b)−(b+a+3)
D. Yes. (3b+3)−(b+a+3)
5. Can two polynomials be subtracted such that the difference is a trinomial? If so, give an example.
A. No. Two polynomials can never be subtracted such that the difference is a trinomial.
B. Yes. (3x+3)−(2x+2y+4)
C. Yes. (3x+3)−(2x+y+3)
D. Yes. (3x+3)−(3x+2y+3)

Answer 1

C. division

Answer 2

1. Polynomials are not closed under which of the following operations?
A. addition
B. multiplication
C. division
D. Subtraction
2. The difference of two polynomials must always result in a _____.
A. Polynomial
B. Monomial
C. Binomial
D. Trinomial
3. Can a binomial be multiplied by a monomial such that the product is a monomial? If so, give an example.
A. Yes. 2(2x+y)=4x+2y
B. Yes. 0(2x+y)=0
C. No. A binomial can never be multiplied by a monomial such that the product is a monomial.
D. Yes. 1(2x+y)=2x+y
4. Can two polynomials be subtracted such that the difference is a binomial? If so, give an example. If not, explain.
A. No. When two polynomials are added from each other, they will always equal a polynomial.
B. No. When two polynomials are subtracted from each other, they always equal a monomial.
C. Yes. (3b^2−3b)−(b+a+3)
D. Yes. (3b+3)−(b+a+3)
5. Can two polynomials be subtracted such that the difference is a trinomial? If so, give an example.
A. No. Two polynomials can never be subtracted such that the difference is a trinomial.
B. Yes. (3x+3)−(2x+2y+4)
C. Yes. (3x+3)−(2x+y+3)
D. Yes. (3x+3)−(3x+2y+3)
please answer all of them

Answer 3

1. A. addition
2. A. Polynomial
3. A. Yes. 2(2x+y)=4x+2y
4. B. No. When two polynomials are subtracted from each other, they always equal a monomial.
5. C. Yes. (3x+3)−(2x+y+3)