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Classify the following polynomials. Combine any like terms first.

[tex]\[
\begin{array}{l}
1. \quad 2x - x^2 + 4x + x^2 \\
2. \quad x^3 - 5x^2 + 3 - 2 \\
3. \quad x^3 - x^3 + x^2 - x^2 + 3 \\
4. \quad 7x - x^2 + x^3 + 4x^2 \\
5. \quad -6x - x^3 + 6x - 4x
\end{array}
\][/tex]

[tex]\[
\begin{array}{c}
\square \\
\square \\
\square \\
\square \\
\square
\end{array}
\][/tex]

Sagot :

GinnyAnsweridn
Let's classify each polynomial by combining the like terms first and then determining its degree.

1. Polynomial: [tex]\(2x - x^2 + 4x + x^2\)[/tex]

Step-by-step simplification:
[tex]\[ 2x - x^2 + 4x + x^2 \][/tex]
Combine the like terms:
[tex]\[ (2x + 4x) + (-x^2 + x^2) \][/tex]
Simplified:
[tex]\[ 6x + 0 = 6x \][/tex]
Degree: 1

2. Polynomial: [tex]\(x^3 - 5x^2 + 3 - 2\)[/tex]

Step-by-step simplification:
[tex]\[ x^3 - 5x^2 + 3 - 2 \][/tex]
Combine the like terms:
[tex]\[ x^3 - 5x^2 + (3 - 2) \][/tex]
Simplified:
[tex]\[ x^3 - 5x^2 + 1 \][/tex]
Degree: 3

3. Polynomial: [tex]\(x^3 - x^3 + x^2 - x^2 + 3\)[/tex]

Step-by-step simplification:
[tex]\[ x^3 - x^3 + x^2 - x^2 + 3 \][/tex]
Combine the like terms:
[tex]\[ (x^3 - x^3) + (x^2 - x^2) + 3 \][/tex]
Simplified:
[tex]\[ 0 + 0 + 3 = 3 \][/tex]
Degree: 0

4. Polynomial: [tex]\(7x - x^2 + x^3 + 4x^2\)[/tex]

Step-by-step simplification:
[tex]\[ 7x - x^2 + x^3 + 4x^2 \][/tex]
Combine the like terms:
[tex]\[ x^3 + (-x^2 + 4x^2) + 7x \][/tex]
Simplified:
[tex]\[ x^3 + 3x^2 + 7x \][/tex]
Degree: 3

5. Polynomial: [tex]\(-6x - x^3 + 6x - 4x\)[/tex]

Step-by-step simplification:
[tex]\[ -6x - x^3 + 6x - 4x \][/tex]
Combine the like terms:
[tex]\[ -x^3 + (-6x + 6x - 4x) \][/tex]
Simplified:
[tex]\[ -x^3 - 4x \][/tex]
Degree: 3

Now, let's summarize the classification of each polynomial with its degree:

1. [tex]\(6x\)[/tex], Degree: 1
2. [tex]\(x^3 - 5x^2 + 1\)[/tex], Degree: 3
3. [tex]\(3\)[/tex], Degree: 0
4. [tex]\(x^3 + 3x^2 + 7x\)[/tex], Degree: 3
5. [tex]\(-x^3 - 4x\)[/tex], Degree: 3
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