Question

The lengths of two sides of a triangle are shown.

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? Show your work.(4 points)

Part B: What is the length of the third side of the triangle? Show your work. (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: to find the total length of sides 1 and 2, simply add the two polynomials

Side 1: 3x2 − 2x − 1

Side 2: 9x + 2x2 − 3

by combing like terms. for starters, 3x^2 and 2x^2 combine to make 5x^2. continue with the rest of the polynomials

Answer 2

part B: all three side lengths in a triangle sum up to get the perimeter

so to get the third side, subtract

perimeter - side 1 - side 2

using the same logic of combining like terms

Answer 3

part C: for polynomials to be closed under addition and subtraction, polynomials must add/subtract to produce another polynomial. when you performed the operations on polynomials from parts A+B, were your results also polynomials?

if you're not sure, think about what defines a polynomial: an expression, consisting of constants, coefficients, and/or variables where the variables are only raised to positive integer exponents