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Standard Form and Classifying Polynomials

Name: Elayna

1. [tex]\( 9 + 2x^3 - 7x^3 - 2x^3 \)[/tex]

2. [tex]\( -8 + 9x^5 + 8 \)[/tex]

3. [tex]\( 7 \)[/tex]

4. [tex]\( -8 - 5x^3 + 4x^5 - 4x - 6 \)[/tex]

5. [tex]\( -3 - 8x^3 - 6x \)[/tex]

6. [tex]\( 4 + 8x^4 \)[/tex]

7. [tex]\( -8 + 7x^4 \)[/tex]

8. [tex]\( -3x^3 \)[/tex]

9. [tex]\( 8 \)[/tex]

10. [tex]\( 5 - 8x \)[/tex]

11. [tex]\( 5 + 7x^5 \)[/tex]

12. [tex]\( 5 \)[/tex]

13. [tex]\( -9x^5 - 7x \)[/tex]

14. [tex]\( 4x + x \)[/tex]

15. [tex]\( 9 - 3x^5 - 2x^2 \)[/tex]

16. [tex]\( -x^2 \)[/tex]

17. [tex]\( 4x^3 + 9x^4 + 7 \)[/tex]

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

19. [tex]\( -9x^4 + 7x^4 - 8 \)[/tex]

20. [tex]\( 3 - 4x^3 + 1 \)[/tex]



Answer :

GinnyAnswer
Let's simplify and classify each polynomial in terms of its standard form and degree.

### Process

1. Simplify each polynomial to its standard form:
- Combine like terms.
- Arrange the terms in descending order according to the degree of [tex]\( x \)[/tex].

2. Classify each polynomial based on its degree:
- Degree 0: Constant polynomial
- Degree 1: Linear polynomial
- Degree 2: Quadratic polynomial
- Degree 3: Cubic polynomial
- Degree 4: Quartic polynomial
- Degree 5: Quintic polynomial

### Simplification and Classification

1. [tex]\( 9 + 2x^3 - 7x^3 - 2x^3 \)[/tex]
- Simplify: [tex]\( 9 + (2 - 7 - 2)x^3 = 9 - 7x^3 \)[/tex]
- Standard form: [tex]\( 9 - 7x^3 \)[/tex]
- Degree: 3 (Cubic)

2. [tex]\( -8 + 9x^5 + 8 \)[/tex]
- Simplify: [tex]\( (-8 + 8) + 9x^5 = 9x^5 \)[/tex]
- Standard form: [tex]\( 9x^5 \)[/tex]
- Degree: 5 (Quintic)

3. [tex]\( 7 \)[/tex]
- Simplify: [tex]\( 7 \)[/tex]
- Standard form: [tex]\( 7 \)[/tex]
- Degree: 0 (Constant)

4. [tex]\( -8 - 5x^3 + 4x^5 - 4x - 6 \)[/tex]
- Simplify: [tex]\( (-8 - 6) + 4x^5 - 5x^3 - 4x = -14 + 4x^5 - 5x^3 - 4x \)[/tex]
- Standard form: [tex]\( 4x^5 - 5x^3 - 4x - 14 \)[/tex]
- Degree: 5 (Quintic)

5. [tex]\( -3 - 8x^3 - 6x \)[/tex]
- Simplify: [tex]\( -3 - 8x^3 - 6x \)[/tex]
- Standard form: [tex]\( -8x^3 - 6x - 3 \)[/tex]
- Degree: 3 (Cubic)

6. [tex]\( 4 + 8x^4 \)[/tex]
- Simplify: [tex]\( 4 + 8x^4 \)[/tex]
- Standard form: [tex]\( 8x^4 + 4 \)[/tex]
- Degree: 4 (Quartic)

7. [tex]\( -8 + 7x^4 \)[/tex]
- Simplify: [tex]\( -8 + 7x^4 \)[/tex]
- Standard form: [tex]\( 7x^4 - 8 \)[/tex]
- Degree: 4 (Quartic)

8. [tex]\( -3x^3 \)[/tex]
- Simplify: [tex]\( -3x^3 \)[/tex]
- Standard form: [tex]\( -3x^3 \)[/tex]
- Degree: 3 (Cubic)

9. [tex]\( 8 \)[/tex]
- Simplify: [tex]\( 8 \)[/tex]
- Standard form: [tex]\( 8 \)[/tex]
- Degree: 0 (Constant)

10. [tex]\( 5 - 8x \)[/tex]
- Simplify: [tex]\( 5 - 8x \)[/tex]
- Standard form: [tex]\( -8x + 5 \)[/tex]
- Degree: 1 (Linear)

11. [tex]\( 5 + 7x^5 \)[/tex]
- Simplify: [tex]\( 5 + 7x^5 \)[/tex]
- Standard form: [tex]\( 7x^5 + 5 \)[/tex]
- Degree: 5 (Quintic)

12. [tex]\( 5 \)[/tex]
- Simplify: [tex]\( 5 \)[/tex]
- Standard form: [tex]\( 5 \)[/tex]
- Degree: 0 (Constant)

13. [tex]\( -9x^5 - 7x \)[/tex]
- Simplify: [tex]\( -9x^5 - 7x \)[/tex]
- Standard form: [tex]\( -9x^5 - 7x \)[/tex]
- Degree: 5 (Quintic)

14. [tex]\( 4x + x \)[/tex]
- Simplify: [tex]\( 4x + x = 5x \)[/tex]
- Standard form: [tex]\( 5x \)[/tex]
- Degree: 1 (Linear)

15. [tex]\( 9 - 3x^5 - 2x^2 \)[/tex]
- Simplify: [tex]\( 9 - 3x^5 - 2x^2 \)[/tex]
- Standard form: [tex]\( -3x^5 - 2x^2 + 9 \)[/tex]
- Degree: 5 (Quintic)

16. [tex]\( -x^2 \)[/tex]
- Simplify: [tex]\( -x^2 \)[/tex]
- Standard form: [tex]\( -x^2 \)[/tex]
- Degree: 2 (Quadratic)

17. [tex]\( 4x^3 + 9x^4 + 7 \)[/tex]
- Simplify: [tex]\( 4x^3 + 9x^4 + 7 \)[/tex]
- Standard form: [tex]\( 9x^4 + 4x^3 + 7 \)[/tex]
- Degree: 4 (Quartic)

18. [tex]\( 2 \)[/tex]
- Simplify: [tex]\( 2 \)[/tex]
- Standard form: [tex]\( 2 \)[/tex]
- Degree: 0 (Constant)

19. [tex]\( -9x^4 + 7x^4 - 8 \)[/tex]
- Simplify: [tex]\( (-9x^4 + 7x^4) - 8 = -2x^4 - 8 \)[/tex]
- Standard form: [tex]\( -2x^4 - 8 \)[/tex]
- Degree: 4 (Quartic)

20. [tex]\( 3 - 4x^3 + 1 \)[/tex]
- Simplify: [tex]\( 3 + 1 - 4x^3 = 4 - 4x^3 \)[/tex]
- Standard form: [tex]\( -4x^3 + 4 \)[/tex]
- Degree: 3 (Cubic)

This way, each polynomial is simplified and classified according to its degree.

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