Question

The lengths of two sides of a triangle are shown below:

Side 1: 8x2 - 5x - 2
Side 2: 7x - x2 + 3

The perimeter of the triangle is 4x3 - 3x2 + 2x - 6.

Part A: What is the total length of the two sides, 1 and 2, of the triangle? (4 points)

Part B: What is the length of the third side of the triangle? (4 points)

Part C: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction? Justify your answer. (2 points)

Answer 1

Side 1: 8\(x^2\) - 5x - 2
Side 2: 7x - x2 + 3

part A
total length of the two sides is Side1 + Side2 => (8\(x^2) - 5x - 2) + (7x - x2 + 3)

Answer 2

part B

well... we know the perimeter of a shape is ALL SIDES summed up together

so Side1 + Side2 + Side3 = perimeter

if you subtract Side1 and Side2 from the perimeter, you'd end up with
\(\bf \cancel{ Side1 + Side2 } + {\color{brown}{ Side3}} -(\cancel{ Side1 + Side2 } )\)

Answer 3

part C

well..... check the polynomials form part A and part B
see if they nicely fit within their addition, no matter how you arrange them

Answer 4

How would I do that

Answer 5

part C?

Answer 6

yes

Answer 7

well to be closed under the addition operation means

if you add part B and part C, in any way, B +C or C + B
then what you will end up will be YET ANOTHER polynomial

and if you subtract part B and C, in any way, B - C or C - B
then you will also end up with YET ANOTHER polynomial

if that's the case, their addition and subtraction yields another polynomial
then they're said to be CLOSED under addition and subtraction

Answer 8

hmmm anyhow... I mean.. part A and B =)

Answer 9

well to be closed under the addition operation means

if you add part B and part A, in any way, B +A or A + B
then what you will end up will be YET ANOTHER polynomial

and if you subtract part B and A, in any way, B - A or A - B
then you will also end up with YET ANOTHER polynomial

if that's the case, their addition and subtraction yields another polynomial
then they're said to be CLOSED under addition and subtraction

Answer 10

for part a do I add them