College

Which of the following correctly lists the terms of the polynomial [tex]12x^3 - 6x^2 + 4x - 9[/tex]?

A. [tex]12x^3, 6x^2, 4x[/tex]
B. [tex]12x^3, 6x^2, 4x, 9[/tex]
C. [tex]12x^3, -6x^2, 4x, -9[/tex]
D. [tex]12x^3, -6x^2, 4x[/tex]

Answer :

To solve this question, let's break down the polynomial and identify its terms.

The polynomial provided is:

[tex]\[ 12x^3 - 6x^2 + 4x - 9 \][/tex]

A polynomial consists of several terms. Each term is a part of the expression separated by a plus (+) or minus (−) sign. Let's identify each term in this polynomial:

1. The first term is [tex]\( 12x^3 \)[/tex]. This term includes the coefficient (12) and the variable part [tex]\( x^3 \)[/tex].

2. The second term is [tex]\(-6x^2 \)[/tex]. The negative sign should be included with the term, so it is [tex]\(-6x^2\)[/tex].

3. The third term is [tex]\(4x\)[/tex]. There's no sign in front of it, so it remains positive.

4. The fourth term is [tex]\(-9\)[/tex]. Again, the negative sign is part of the term, so it is [tex]\(-9\)[/tex].

Now let's list the terms as they appear in the polynomial, taking care to include any negative signs:

- [tex]\( 12x^3 \)[/tex]

- [tex]\(-6x^2\)[/tex]

- [tex]\(4x\)[/tex]

- [tex]\(-9\)[/tex]

Therefore, the correct listing of the terms of the polynomial [tex]\( 12x^3 - 6x^2 + 4x - 9 \)[/tex] is:

[tex]\[ 12x^3, -6x^2, 4x, -9 \][/tex]

Thus, the correct answer is the third option:

[tex]\(12x^3, -6x^2, 4x, -9\)[/tex].