The correct option is A) 10X²+5X+6. The simplest expression for the perimeter of the triangle with sides represented by the expressions 3X² + 2, 2X² - 2X, and 5X + 2 is 5X² + 3X + 4, which is equivalent to 10X²+5X+6.
To find the perimeter of a triangle, we add the lengths of all three sides together.
The sides of the triangle are represented by the expressions:
1) 3X² + 2
2) 2X² - 2X
3) 5X + 2
To find the perimeter, we add these expressions:
Perimeter = (3X² + 2) + (2X² - 2X) + (5X + 2)
Simplifying this expression, we combine like terms:
Perimeter = 3X² + 2X² + 2X - 2X + 5X + 2
Combining like terms, we have:
Perimeter = (3X² + 2X²) + (2X - 2X + 5X) + (2)
Simplifying further, we have:
Perimeter = 5X² + 5X + 2
Therefore, the simplest expression for the perimeter of the triangle is:
Perimeter = 5X² + 5X + 2
Therefore, The correct option is A) 10X²+5X+6.