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Name: Ashylen Machuca
Date: [tex]$1-8-25$[/tex]
Period: AC

**POLYNOMIALS**

Rewrite each polynomial in standard form. Then classify by degree and number of terms.

1. [tex]3x + 4x^3 - 9x^2[/tex]
- Standard Form: [tex]4x^3 - 9x^2 + 3x[/tex]
- Classification: Cubic Trinomial

2. [tex]3 - x^4 + x^3 - 2x[/tex]
- Standard Form: [tex]-x^4 + x^3 - 2x + 3[/tex]
- Classification: Quartic Polynomial

3. [tex]x - 15x^5[/tex]
- Standard Form: [tex]-15x^5 + x[/tex]
- Classification: Quintic Binomial

4. [tex]2x^2[/tex]
- Classification: Quadratic Monomial

5. [tex]8a^3 - 5a + 4[/tex]
- Classification: Cubic Trinomial

6. [tex]y^2 + 8 - y[/tex]
- Standard Form: [tex]y^2 - y + 8[/tex]
- Classification: Quadratic Trinomial

7. [tex]2 - \frac{1}{2}x[/tex]
- Classification: Linear Binomial

8. [tex]-5[/tex]
- Classification: Constant Monomial

9. [tex]8x^3 + 64[/tex]
- Classification: Cubic Binomial

10. [tex]3x^2 - 2x^3 + 45 - 7x[/tex]
- Standard Form: [tex]-2x^3 + 3x^2 - 7x + 45[/tex]
- Classification: Cubic Polynomial

Answer :

Let's rewrite each polynomial in standard form and classify them by their degree and the number of terms.

1. Polynomial: [tex]\(3x + 4x^3 - 9x^2\)[/tex]
- Standard Form: Arrange terms from highest to lowest degree: [tex]\(4x^3 - 9x^2 + 3x\)[/tex].
- Classification:
- Degree: 3 (Cubic)
- Number of terms: 3 (Trinomial)

2. Polynomial: [tex]\(3 - x^4 + x^3 - 2x\)[/tex]
- Standard Form: [tex]\(-x^4 + x^3 - 2x + 3\)[/tex].
- Classification:
- Degree: 4 (Quartic)
- Number of terms: 4 (Polynomial)

3. Polynomial: [tex]\(x - 15x^5\)[/tex]
- Standard Form: [tex]\(-15x^5 + x\)[/tex].
- Classification:
- Degree: 5
- Number of terms: 2 (Binomial)

4. Polynomial: [tex]\(2x^2\)[/tex]
- Standard Form: Already in standard form as [tex]\(2x^2\)[/tex].
- Classification:
- Degree: 2 (Quadratic)
- Number of terms: 1 (Monomial)

5. Polynomial: [tex]\(8a^3 - 5a + 4\)[/tex]
- Standard Form: Already in standard form as [tex]\(8a^3 - 5a + 4\)[/tex].
- Classification:
- Degree: 3 (Cubic)
- Number of terms: 3 (Trinomial)

6. Polynomial: [tex]\(y^2 + 8 - y\)[/tex]
- Standard Form: Reorder terms: [tex]\(y^2 - y + 8\)[/tex].
- Classification:
- Degree: 2 (Quadratic)
- Number of terms: 3 (Trinomial)

7. Polynomial: [tex]\(2 - \frac{1}{2}x\)[/tex]
- Standard Form: [tex]\(-\frac{1}{2}x + 2\)[/tex].
- Classification:
- Degree: 1 (Linear)
- Number of terms: 2 (Binomial)

8. Polynomial: [tex]\(-5\)[/tex]
- Standard Form: Already in standard form as [tex]\(-5\)[/tex].
- Classification:
- Degree: 0 (Constant)
- Number of terms: 1 (Monomial)

9. Polynomial: [tex]\(8x^3 + 64\)[/tex]
- Standard Form: Already in standard form as [tex]\(8x^3 + 64\)[/tex].
- Classification:
- Degree: 3 (Cubic)
- Number of terms: 2 (Binomial)

10. Polynomial: [tex]\(3x^2 - 2x^3 + 45 - 7x\)[/tex]
- Standard Form: [tex]\(-2x^3 + 3x^2 - 7x + 45\)[/tex].
- Classification:
- Degree: 3 (Cubic)
- Number of terms: 4 (Polynomial)

Each polynomial is rearranged to standard form and classified based on its degree and the number of terms it contains.

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