Question

A right triangle has base (x - 5) units and height (4x - 10) units.

Part A: What is the square of the length of the hypotenuse of the triangle?
Part B: What is the area of the triangle?
Part C: Using the solution obtained in Part B, explain the closure property of multiplication of polynomials.

Answer 1

well for A using pythagoras' theorem

\[h^2 = (4x -10)^2 + (x -5)^2\]

for B

the area

\[A = \frac{1}{2} \times (x -5)(4x -10)\]

Answer 2

I understand all that but idk what c is

Answer 3

all that is is says is that if you multiply 2 polynomials then you get a polynomial as an answer...

if you add 2 polynomials you still get a polynomial.

so using pythagoras' theorem squaring each polynomial will result in a degree 2 polynomial then adding the 2 degree 2 polynomials still results in a polynomial so it is a closed operation.

the area question, you have degree 0 polynomial, degree 1 polynomial and degree 1 polynomial so multiplying them will result in a polynomial of degree 2

hope it makes sense