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Degree Of A Polynomial

The degree of a polynomial is the highest power of the variable present in the polynomial expression. For a polynomial in one variable, it is the largest exponent of that variable which has a non-zero coefficient.

Key Concepts

Based on their degree, polynomials are classified as linear (degree 1), quadratic (degree 2), and cubic (degree 3).
The degree of a polynomial indicates the maximum number of real zeroes or roots the polynomial can have.
A non-zero constant polynomial has a degree of 0, whereas the degree of a zero polynomial is undefined.

Formula & Equation

ForP(x)=anxn+a(nāˆ’1)x(nāˆ’1)+...+a1x+a0,whereanisnotequalto0,thedegreeisn.For P(x) = a_n x^n + a_(n-1) x^(n-1) + ... + a_1 x + a_0, where a_n is not equal to 0, the degree is n.

P(x) is the polynomial, x is the variable, n is the highest exponent representing the degree, and a_n is the leading coefficient.

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Common Misconceptions

Myth: The degree of a polynomial is the sum of all the exponents in the expression.
Fact: For a polynomial in one variable, the degree is strictly the single highest exponent present, not the sum of all exponents.

Real World Applications

The path of a projectile, like a thrown basketball, is modeled by a quadratic polynomial of degree 2.
Calculating a taxi fare with a fixed base rate and a per-kilometer charge uses a linear polynomial of degree 1.

Frequently Asked Questions

Can the degree of a polynomial be a negative number or a fraction?
No, the exponents of the variables in a polynomial must be whole numbers, so the degree cannot be negative or a fraction.
What is the degree of a zero polynomial?
The degree of a zero polynomial is not defined.

Keep Learning

Linear PolynomialQuadratic PolynomialCubic Polynomial