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)
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)
C. division
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
1. Polynomials are not closed under the operation of C. division. Dividing one polynomial by another may result in a quotient that is not a polynomial.
2. The difference of two polynomials must always result in a A. Polynomial.
3. Yes. A monomial can be multiplied by a binomial to give a monomial. An example is given in option A. 2(2x+y)=4x+2y.
4. Yes. Two polynomials can be subtracted such that the difference is a binomial. An example is given in option C. (3b^2−3b)−(b+a+3).
5. Yes. Two polynomials can be subtracted such that the difference is a trinomial. An example is given in option D. (3x+3)−(3x+2y+3).