The set of polynomials is closed under the operation of subtraction.
a: which equations illustrate this concept?
b: which statements correctly explain this concept?
there may be more than one correct answer for each question. select all correct answers for each question.
a:
(3x+4)+(5x−5)=8x−1
(3x+4)+(5x−5)=8x−1
a:
(3x−4)−(2x+2)=x−6
(3x−4)−(2x+2)=x−6
b: the product of the polynomials
(3x)
(3x)
and
(2x+2)
(2x+2)
is a polynomial,
6
x
2
+6x
6x2+6x
, which shows there is closure under subtraction.
a:
(3x)(2x+2)=6
x
2
+6x
(3x)(2x+2)=6x2+6x
b: the difference of the polynomials
(3x−4)
(3x−4)
and
(2x+2)
(2x+2)
is a polynomial,
x−6
x−6
, which shows there is closure under subtraction.
b: the sum of the polynomials
(3x+4)
(3x+4)
and
(5x−5)
(5x−5)
is a polynomial,
8x−1
8x−1
, which shows there is closure under subtraction.
b: the difference of the polynomials
(x−2)
(x−2)
and
(3x+1)
(3x+1)
is a polynomial,
−2x−3
−2x−3
, which shows there is closure under subtraction.
a:
(x−2)−(3x+1)=−2x−3