Which polynomial is equivalent to (x^3+2x^4+5x^5-2x--x^2+9x^3+2x^4)?
a. 5x^5+10x^3+x^2-9x-1
b. 5x^5-8x^3+x^2+5x-1
c. 5x^5-8x^3+x^2+5x+1
d. 5x^5+4x^4+10x^3+x^2-9x-1
e. 5x^5-4x^4-8x^3+x^2+5x+1

The correct answer is option B.

5x⁵ + -8x³ + x² + 5x -1

Step-by-step explanation:

It is given that,

(x³ + 2x⁴ + 5x⁵ - 2x - 1) - (-7x - x² + 9x³ + 2x⁴)

To find the subtraction result

(x³ + 2x⁴ + 5x⁵ - 2x - 1) - (-7x - x² + 9x³ + 2x⁴)

 = x³ + 2x⁴ + 5x⁵ - 2x - 1 + 7x + x² - 9x³ - 2x⁴)

 = 5x⁵ + 2x⁴ - 2x⁴ + x³ - 9x³  + x²- 2x + 7x -1

 = 5x⁵ + -8x³ + x² + 5x -1

The correct answer is option B.

5x⁵ + -8x³ + x² + 5x -1