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Classify each polynomial as constant, linear, quadratic, or cubic. Combine like terms first.

[tex]\[
\begin{array}{l}
1. x^3 - 2x + x^3 \\
2. 4x^2 - 6x - 8x^2 \\
3. 6x - 6 + 6x \\
4. 5 + 4x^2 - 4x^2 + 5
\end{array}
\][/tex]

1. [tex]\(\square\)[/tex]

2. [tex]\(\square\)[/tex]

3. [tex]\(\square\)[/tex]

4. [tex]\(\square\)[/tex]



Answer :

GinnyAnswer
To classify each polynomial as constant, linear, quadratic, or cubic, we need to combine the like terms first. Let’s analyze each polynomial step by step:

1. Polynomial: [tex]\( x^3 - 2x + x^3 \)[/tex]
- Combine the like terms:
[tex]\[ x^3 + x^3 - 2x = 2x^3 - 2x \][/tex]
- Degree of the polynomial:
- The highest power of [tex]\( x \)[/tex] is 3.
- Classification:
[tex]\[ \text{Cubic} \][/tex]

2. Polynomial: [tex]\( 4x^2 - 6x - 8x^2 \)[/tex]
- Combine the like terms:
[tex]\[ 4x^2 - 8x^2 - 6x = -4x^2 - 6x \][/tex]
- Degree of the polynomial:
- The highest power of [tex]\( x \)[/tex] is 2.
- Classification:
[tex]\[ \text{Quadratic} \][/tex]

3. Polynomial: [tex]\( 6x - 6 + 6x \)[/tex]
- Combine the like terms:
[tex]\[ 6x + 6x - 6 = 12x - 6 \][/tex]
- Degree of the polynomial:
- The highest power of [tex]\( x \)[/tex] is 1.
- Classification:
[tex]\[ \text{Linear} \][/tex]

4. Polynomial: [tex]\( 5 + 4x^2 - 4x^2 + 5 \)[/tex]
- Combine the like terms:
[tex]\[ 5 + 5 + 4x^2 - 4x^2 = 10 \][/tex]
- Degree of the polynomial:
- There is no [tex]\( x \)[/tex] term, so the degree is 0.
- Classification:
[tex]\[ \text{Constant} \][/tex]

Therefore, the classifications are:
1. [tex]\( 2x^3 - 2x \)[/tex] → Cubic
2. [tex]\( -4x^2 - 6x \)[/tex] → Quadratic
3. [tex]\( 12x - 6 \)[/tex] → Linear
4. [tex]\( 10 \)[/tex] → Constant

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