Question

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

Side 1: 3x2 − 2x − 1

Side 2: 9x + 2x2 − 3

The perimeter of the triangle is 5x3 + 4x2 − x − 3.

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

Part A Just add like terms :-
3x^2 - 2x - 1 + 9x + 2x^2 - 3

Answer 2

this is what i have so far:


Part A: ](3x2 − 2x − 1)+(9x + 2x2 − 3)
3x2−2x−1+9x+2x2−3
=3x2+−2x+−1+9x+2x2+−3
Combine Like Terms:
=3x2+−2x+−1+9x+2x2+−3
=(3x2+2x2)+(−2x+9x)+(−1+−3)
=5x2+7x+−4
Answer:
=5x2+7x−4
Part B:]
5x3+4x2−x−3−(5x2+7x−4)
Distribute the Negative Sign:
=5x3+4x2−x−3+−1(5x2+7x−4)
=5x3+4x2+−x+−3+−1(5x2)+−1(7x)+(−1)(−4)
=5x3+4x2+−x+−3+−5x2+−7x+4
Combine Like Terms:
=5x3+4x2+−x+−3+−5x2+−7x+4
=(5x3)+(4x2+−5x2)+(−x+−7x)+(−3+4)
=5x3+−x2+−8x+1
Answer:
=5x3−x2−8x+1

Answer 3

Par5 B
subtract the result from the above addition from the expression for the perimeter.

Answer 4

yah i just dont knoow what part c is supposed to mean

Answer 5

yes those 2 parts are correct

Answer 6

thanks but do you know what part c means?

Answer 7

polynomials being closed under addition and subtraction means that if you add or subtract polynomials then the result is another polynomial.

Answer 8

so in your case do the results support this?

Answer 9

yeah

Answer 10

yea they do Thats all there is to Part C.

Answer 11

thanks!

Answer 12

thanks!

Answer 13

Part C:
Yes, when i added side 2 and side 1 i got 5x2+7x−4 which is another plynomial

Answer 14

does that sound good @welshfella