Question

the lengths of 2 sides of a triangle are shown. side 1: 3x2 - 4x - 1. side 2: 4x - x2 + 5. the perimeter is 5x3 - 2x2 + 3x - 8

Answer 1

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