Question

What is the additive inverse of the polynomial -9x²ʸ + 6x²ʸ - 5x³?

A) 9x²ʸ - 6x²ʸ + 5x³
B) -9x²ʸ - 6x²ʸ - 5x³
C) -9x²ʸ + 6x²ʸ + 5x³
D) 9x²ʸ + 6x²ʸ + 5x³

Answer 1

The additive inverse of the polynomial -9x²˥ + 6x²˥ - 5x³ is 9x²˥ - 6x²˥ + 5x³. This is because the additive inverse requires changing the sign of each term in the original polynomial.

Step-by-step explanation:

The additive inverse of a polynomial is another polynomial such that when they are added together, they yield a sum of zero. To find the additive inverse of a given polynomial, you change the sign of each term in the polynomial. The original polynomial given is -9x²˥ + 6x²˥ - 5x³.

The additive inverse of this polynomial is obtained by changing the sign of each term:

• The additive inverse of -9x²˥ is +9x²˥
• The additive inverse of +6x²˥ is -6x²˥
• The additive inverse of -5x³ is +5x³

Therefore, the correct additive inverse is 9x²˥ - 6x²˥ + 5x³, which corresponds to option A.

Answer 2

The additive inverse of the polynomial -9x²ʸ + 6x²ʸ - 5x³ is A) 9x²ʸ - 6x²ʸ + 5x³.

Step-by-step explanation:

The additive inverse of a polynomial is obtained by changing the sign of each term in the polynomial. In this case, the additive inverse of -9x²ʸ + 6x²ʸ - 5x³ is 9x²ʸ - 6x²ʸ + 5x³, as each term's sign is reversed (Option A).

Understanding the concept of additive inverses is fundamental in algebra. It involves reversing the signs of all terms within the polynomial, which is essential for various algebraic operations, including simplification and solving equations.

Option A is correct.