Question

Subtract. Write your answer in standard form.

(5x^3 - 2x^2 + 7x - 11) - (-8x^3 - 11x^2 - 5x + 2)
a) 13x^3 + 9x^2 + 12x - 13
b) -3x^3 + 9x^2 + 12x - 13
c) -13x^3 - 9x^2 - 12x + 13
d) 3x^3 - 9x^2 - 12x - 13

Answer 1

The correct standard form of the polynomial after subtraction is 13x^3 + 9x^2 + 12x - 13.

Step-by-step explanation:

To subtract the polynomial (5x^3 - 2x^2 + 7x - 11) from (-8x^3 - 11x^2 - 5x + 2), we need to change the sign of each term in the second polynomial and add it to the corresponding term in the first polynomial:

• (5x^3) - (-8x^3) = 5x^3 + 8x^3 = 13x^3
• (-2x^2) - (-11x^2) = -2x^2 + 11x^2 = 9x^2
• (7x) - (-5x) = 7x + 5x = 12x
• (-11) - (+2) = -11 - 2 = -13

Combining these terms gives us the final answer in standard form: 13x^3 + 9x^2 + 12x - 13.