Answer:

ACTIVITY 1: Let's Practice!

1. 2x³ + 9x² + 3x + 1 = 0

- This equation is a polynomial because it consists of terms with non-negative integer exponents.

2. x³ + 3x² + 2x - 1 = 0

- This equation is a polynomial because it consists of terms with non-negative integer exponents.

3. 6x⁴ + 7x⁵ + 3 = 0

- This equation is a polynomial because it consists of terms with non-negative integer exponents.

4. 3x² + 2x½ + 4 = 0

- This equation is not a polynomial because it contains a term with a fractional exponent (x^(1/2)).

5. x⁴ - √3x + 1 = 0

- This equation is a polynomial because it consists of terms with non-negative integer exponents. The square root (√) does not affect the polynomial nature of the equation.

ACTIVITY 2: Keep Practicing!

1. x² + 8x³ + 7 - x = 0

- To write this equation in standard form, we rearrange the terms in descending order of exponents:

8x³ + x² - x + 7 = 0

2. x³ - 3 + 2x⁵ - 2x⁴ = 0

- To write this equation in standard form, we rearrange the terms in descending order of exponents:

2x⁵ - 2x⁴ + x³ - 3 = 0

3. 2x + x³ + x⁵ + 1 - x² = 0

- To write this equation in standard form, we rearrange the terms in descending order of exponents:

x⁵ + x³ - x² + 2x + 1 = 0

4. (x² + 6)(x + 5) = 0

- To write this equation in standard form, we expand the expression:

x³ + 5x² + 6x + 30 = 0

5. x²(x + 7)(x - 2) = 0

- To write this equation in standard form, we expand the expression:

x⁴ + 5x³ - 14x² - 70x = 0

Step-by-step explanation:

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