What is resultant polynomial? Find degree of polynomial from given polynomials 1) x²+x+1 2) x³+x+2x+2 3) 4x³+x

The resultant polynomial is the polynomial obtained when you multiply given polynomials together. 

To find the degree of a polynomial, you identify the highest power of the variable \( x \) in the polynomial.

Let's analyze the degree of each given polynomial separately:

1. For the polynomial \( x^2 + x + 1 \):
   - The highest power of \( x \) is 2.
   - Degree: 2

2. For the polynomial \( x^3 + x + 2x + 2 \) (simplifying to \( x^3 + 3x + 2 \)):
   - The highest power of \( x \) is 3.
   - Degree: 3

3. For the polynomial \( 4x^3 + x \):
   - The highest power of \( x \) is 3.
   - Degree: 3

The degree of the resultant polynomial when multiplying these polynomials is the sum of the degrees of the individual polynomials:

\[ \text{Degree of resultant polynomial} = 2 + 3 + 3 = 8 \]

If you have any questions or need further details, feel free to ask!

Here are some questions you might want to ask next:
1. How do you multiply polynomials?
2. Can you show the steps to multiply these specific polynomials together?
3. What is the significance of the degree of a polynomial?
4. How do you find the resultant of two polynomials?
5. What are some applications of polynomials in real life?

**Tip:** Always simplify polynomials by combining like terms to make calculations easier.

Explore the concept of resultant polynomials and how to find the degree of a polynomial with detailed examples. Learn about polynomial multiplication and degree determination for polynomials such as x²+x+1, x³+x+2x+2, and 4x³+x. Suitable for students in Grades 9-12.

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