Question

The length of a rectangle is (6x2 + 3x - 2) units, and its width is (x3 - 2x + 5) units.

Part A: What is the area of the rectangle? Show your work. (5 points)

Part B: Does the answer for Part A show that polynomials are closed under an operation? Justify your answer. (3 points)

Part C: What is the degree and classification of the expression obtained in Part A? (2 points)

Answer 1

@dan815 @perl @shrutipande9

Answer 2

multiply

Answer 3

when i multiply them two together i get 6x^5+3x^4-14x^3+24x^2+19x-10

Answer 4

\[6 x^5+3 x^4-14 x^3+24 x^2+19 x-10\]

Answer 5

yes

Answer 6

looks good to me

Answer 7

okay so how about part B?

Answer 8

In part A) we exhibited a case when two polynomials are multiplied, the result is also a polynomial . This is evidence that polynomials are 'closed' under multiplication

Answer 9

Thanks and part C is a 5th degree polynomail right?

Answer 10

correct

Answer 11

no.

Answer 12

in general closure means that if you have two things in a set, you operate on them, the result is also in a set.
so for example, if you start with the set of positive integers,
N = { 1,2,3,4,5,... } , and pick two arbitrary elements, add them, the result is also in the set.
Example : 2 ,3 2+3 = 5 , and 5 is in N.

What about subtraction? Is the set closed {1,2,3,4... } closed under subtraction?
Is 3 - 5 in the set?

Answer 13

correct, so the positive integers are not closed under subtraction (or division) .
the positive integers are closed under multiplication and addition

Answer 14

You can show that N is not closed under division.
Pick 2, 3,

is 2 ÷ 3 inside N?

Answer 15

okay i understand can you help me on a different question?

Answer 16

sometimes it is though.
6 ÷ 3= 2 , and 2 is inside N.
But its enough to find one 'counterexample' to say that the set is not closed under an operation.

In math we say its 'sufficient' to find one counterexample.

Answer 17

yes want to make a new post?