MathsDegree of Polynomial – Zero, Constant, Linear, Quadratic, Cubic and Bi-quadratic Polynomial

Degree of Polynomial – Zero, Constant, Linear, Quadratic, Cubic and Bi-quadratic Polynomial

What is Degree of Polynomial?

A degree of a polynomial is the largest degree of any of the terms in the polynomial. For example, the degree of the polynomial x3 + 2×2 – 3 is 3.

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    Degree of Polynomial - Zero, Constant, Linear, Quadratic, Cubic and Bi-quadratic Polynomial

    What is the Degree of a Polynomial?

    The degree of a polynomial is the highest degree of the individual terms in the polynomial. So, for example, the degree of the polynomial x2 + 3x + 2 is 2.

    Degree of Zero Polynomial

    A degree of zero polynomial is a polynomial that has a degree of zero. This means that the polynomial has no terms and no coefficients.

    Types of Polynomial

    Constant Polynomial

    An expression of the form a n xn + a n-1 xn-1 + … + a 2 x2 + a 1 x + a 0 is called a constant polynomial.

    The value of the constant polynomial is a 0 .

    Linear Polynomials

    • A linear polynomial is a polynomial of the form
    • A linear polynomial is a polynomial of the form
    • where a and b are real numbers. The coefficients a and b are called the linear coefficients of the polynomial.

    Quadratic Polynomial

    A quadratic polynomial is a polynomial of the form

    where a, b, and c are real numbers and “x” is a variable. The degree of a quadratic polynomial is two.

    Cubic Polynomial

    A cubic polynomial is a polynomial of degree 3.

    The equation of a cubic polynomial is

    where “a”, “b”, and “c” are constants. The graph of a cubic polynomial is a smooth curve that rises quickly and then levels off.

    Bi-quadratic Polynomial

    • A bi-quadratic polynomial is a polynomial in two variables with the form
    • where is a real number and are real coefficients.

    Types of Polynomials Based on their Degrees

    • A monomial is a polynomial that has a single term.
    • A binomial is a polynomial that has two terms.
    • A trinomial is a polynomial that has three terms.

    How to Find the Degree of a Polynomial?

    The degree of a polynomial is the highest degree of any of the terms in the polynomial. To find the degree of a polynomial, you can use a polynomial division algorithm.

    What is the Importance of the Degree of a Polynomial?

    The degree of a polynomial is the largest degree of any term in the polynomial. The degree is important because it tells you how many terms are in the polynomial and how complex the polynomial is.

    Applications of Degree of a Polynomial

    There are a variety of applications of degree of a polynomial. One application is in real life, where a polynomial may be used to model a situation. For example, a polynomial may be used to model the height of a plant over time. Another application is in mathematics, where a polynomial may be used to solve a problem. For example, a polynomial may be used to solve a system of equations.

    Important Points to Remember

    1. You cannot force someone to change.

    2. You cannot change someone.

    3. You can only change yourself.

    4. If you want someone to change, you must influence them.

    5. The only way to influence someone is to change yourself.

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