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].
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].
