Question

expressions-polynomials-evaluate add subtract polynomials:
(1 point)
which of the following is equal to the opposite of 6x + 9?
a. -(6x + 9)
b. 6x - 9
c. -6x - 9
d. -6x + 9
answer(s): (type one or more letters corresponding to your answer(s), separating multiple answers with commas.)

Explanation:

The opposite (or additive inverse) of a polynomial \(a + b\) is \(-(a + b)\), which simplifies to \(-a - b\) by the distributive property. For the polynomial \(6x + 9\), its opposite is \(-(6x + 9)\), and simplifying that using the distributive property (\(-1\times6x + (-1)\times9\)) gives \(-6x - 9\).

• Option A: \(-(6x + 9)\) is the opposite in its factored form.
• Option C: \(-6x - 9\) is the simplified form of the opposite.

Option B changes only the constant term's sign, not the polynomial's opposite. Option D changes the coefficient of \(x\) but keeps the constant term's sign incorrect for the opposite.

Answer:

A, C