## What is a polynomial in algebra?

Polynomials are sums of terms of the form k⋅xⁿ, where k is any number and n is a positive integer. For example, 3x+2x-5 is a polynomial.

What are the basic theorems in algebra?

fundamental theorem of algebra, Theorem of equations proved by Carl Friedrich Gauss in 1799. It states that every polynomial equation of degree n with complex number coefficients has n roots, or solutions, in the complex numbers.

### Are there theorems in algebra?

The fundamental theorem of algebra also known as d’Alembert’s theorem or the d’Alembert–Gauss theorem states that every non-constant single-variable polynomial with complex coefficients has at least one complex root.

What is the formula of polynomial function?

A polynomial is a function of the form f(x) = anxn + an−1xn−1 + + a2x2 + a1x + a0 . The degree of a polynomial is the highest power of x in its expression. Constant (non-zero) polynomials, linear polynomials, quadratics, cubics and quartics are polynomials of degree 0, 1, 2 , 3 and 4 respectively.

#### What is the difference between algebra and polynomial?

The difference is polynomials include only variables and coefficients with mathematical operations(+, -, ×) but algebraic expressions include irrational numbers in the powers as well.

Is x2 1 x2 a polynomial?

Answer. Answer: x^2 – 1 is not a polynomial as after simplifying it there wil be no variable.

## How do you write a polynomial equation?

To write a polynomial equation, we follow these steps:

1. Write the roots as factors, changing the signs and putting each factor in parentheses.
2. Multiply pairs of roots together using a box to organize the multiplication.
3. Make sure that each factor has been multiplied by every other factor, and.

How do you find a polynomial?

To find the degree of the polynomial, add up the exponents of each term and select the highest sum. The degree is therefore 6.

### Are algebraic expressions polynomials?

Polynomials in one variable are algebraic expressions that consist of terms in the form axn a x n where n is a non-negative (i.e. positive or zero) integer and a is a real number and is called the coefficient of the term. The degree of a polynomial in one variable is the largest exponent in the polynomial.

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