Question

Hi! I need some help Please!
The length of a rectangle is (3x2 + x - 3) units, and its width is (2x3 - 4x + 3) 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

Area = length * width

Answer 2

I really just dont understand part B

Answer 3

Oh ok

Answer 4

heres what i got for A and C:
Part A: (3x2 + x - 3)(2x3 - 4x + 3)=a
16x^5+2x^4−18x^3+5x^2+15x−9
Part B:
Part C: Its a 5th degree

Answer 5

i just dont understand what Part B really means.

Answer 6

Yeah that's what I'm trying to figure out. Give me a second to look it up.

Answer 7

no prob, thanks ^_^

Answer 8

This is what I found :
Closure under Addition: (2x2 + 3x + 4) + (x2 - 5x - 3) = 3x2 - 2x + 1
When adding polynomials, the variables and their exponents do not change. Only their coefficients will possibly change. This guarantees that the sum has variables and exponents which are already classified as belonging to polynomials. Polynomials are closed under addition.

• Closure under Subtraction: (2x2 + 3x + 4) - (x2 - 5x - 3) = x2 + 8x + 7
When subtracting polynomials, the variables and their exponents do not change. Only their coefficients will possibly change. This guarantees that the difference has variables and exponents which are already classified as belonging to polynomials. Polynomials are closed under subtraction.

• Closure under Multiplication: (x + 1)(x2 + 4x + 3) = x3 + 5x2 + 7x + 3
When multiplying polynomials, the variables' exponents are added, according to the rules of exponents. Remember that the exponents in polynomials are whole numbers. The whole numbers are closed under addition, which guarantees that the new exponents will be whole numbers. Consequently, polynomials are closed under multiplication.

Source: http://mathbitsnotebook.com/Algebra1/Polynomials/POpolys.html

Answer 9

I think you'll be using Closure under Multiplication in your case.

Answer 10

Right, Thanks so much, it makes sense now! :D