Answer:
A. 2x^2+4
B. 5x^3 - 4x^2 + 3x - 12
C. Yes
Step-by-step explanation:
Given:
Side 1=3x^2-4x-1
Side 2=4x-x^2+5
Perimeter=5x^3-2x^2+3x-8
Perimeter=side 1 + Side 2 + Side 3
A. Total lenght of the two sides
Side 1 + Side 2=(3x^2-4x-1) + (4x-x^2+5)
=3x^2 - 4x - 1 + 4x - x^2 + 5
=3x^2 - x^2 - 4x + 4x - 1 + 5
=2x^2+4
B. Length of the third side
Perimeter=side 1 + Side 2 + Side 3
Recall,
Side 1 + side 2=2x^2+4
Perimeter= (side 1 + Side 2) + Side 3
5x^3-2x^2+3x-8 = 2x^2+4 + side 3
5x^3-2x^2+3x-8 - (2x^2+4) = side
3
5x^3 - 2x^2 + 3x - 8 - 2x^2 - 4 = Side 3
5x^3 - 2x^2 - 2x^2 + 3x - 8 - 4 = Side 3
=5x^3-4x^2+3x-12
Side 3= 5x^3 - 4x^2 + 3x - 12
C. Yes, addition and subtraction of polynomial of the same degree will give result of the same degree or lower degree
