Solving Polynomial Equations

In mathematics, a polynomial is like a treasure map, leading us through the world of variables and exponents. Let’s embark on this journey!

Polynomials are magical expressions in the form of ax^b, where a is a real number and b is a non-negative number. Behold:

• Here is a Polynomial: Example: x⁹ + 5x³ + 4
• A Non-Polynomial: Example: x^-1 + 5x^-3 + 4

The General terms will be:

a_nxⁿ + a_n-1xⁿ⁺¹ + …. + a₂x² + a₁x + a₀

Notably, a_n ≠ 0.
The degree is: n
The leading coefficient is: a_n
The constant term is: a₀

Explanation:

What you should know:

1. A monomial is a polynomial with one term, like 8x⁴.
2. A binomial is a polynomial with two terms, such as 6x⁵ – 13.

Let’s uncover the secrets of adding polynomials:

a) Example 1: Adding a polynomial is like a puzzle! Check out this example:

Add a polynomial: ( x² + 7x + 9 ) + ( 4x⁷ + 5x² + 8 )
Solution:

b) Examples: Now, let’s tackle the multiplication of polynomials:

Multiplying Polynomials: ( x⁵ + 4 ) ( -x⁷ + 7x + 1 )
Solution:

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