arent they the same thing?
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Hello,
A polynomial is a sum of monomials.
A monomial is the product of a constant and a power of a variable (generally x).
e.g.
21x³ is a monomial with 21 as the constant (also called coefficient) and x³ as the power.
2x/3 is a monomial with ⅔ as coefficient and x as the power.
-102.012 x is a monomial with -102.012 as coefficient and x as the power.
x²√5 is a monomial with √5 as coefficient and x² as the power.
By extension, you could also say that a constant value is a monomial since:
5 = 5 × 1 = 5 × xº = 5xº
but nobody really care about constants so...
The degree of a monomial is the power of the variable:
e.g.
21x³ is a monomial of degree 3 since x³ is the power.
2x/3 is a monomial of degree 1 since x=x¹ is the power.
-102.012 x is a monomial of degree 1 since x=x¹ is the power.
x²√5 is a monomial of degree 2 since x² is the power.
A polynomial is a sum of monomials.
e.g.
21x³ + 2x/3 + 5 is a polynomial.
x²√5 - 102.012 x is a polynomial.
21x³ + x²√5 + 2x/3 + 5 is a polynomial.
But:
21x³ is also a polynomial since it is also the sum of 21x³ and 0.x²
So every monomial is a polynomial.
The degree of a polynomial is the highest degree of all non-nil monomials it is the sum of:
e.g.
21x³ + 2x/3 + 5 is a polynomial of degree 3 since x³>x¹>xº
x²√5 - 102.012 x is a polynomial of degree 2 since x²>x¹
(25 - 5²)x³ + x² + 5 is a polynomial of degree 2 since x²>xº (the coefficient of x³ is nil!)
A quadratic is a polynomial of degree 2.
e.g
(25 - 5²)x³ + x² + 5 is a quadratic.
x²√5 - 102.012 x is a quadratic.
So a polynomial is not the same thing as a quadratic.
A quadratic is always a polynomial but a polynomial is not always a quadratic.
If you need an analogy:
A chihuahua is always a dog. But not all dogs are chihuahuas.
Explicatively,
Dragon.Jade :-)
A polynomial is a sum of monomials.
A monomial is the product of a constant and a power of a variable (generally x).
e.g.
21x³ is a monomial with 21 as the constant (also called coefficient) and x³ as the power.
2x/3 is a monomial with ⅔ as coefficient and x as the power.
-102.012 x is a monomial with -102.012 as coefficient and x as the power.
x²√5 is a monomial with √5 as coefficient and x² as the power.
By extension, you could also say that a constant value is a monomial since:
5 = 5 × 1 = 5 × xº = 5xº
but nobody really care about constants so...
The degree of a monomial is the power of the variable:
e.g.
21x³ is a monomial of degree 3 since x³ is the power.
2x/3 is a monomial of degree 1 since x=x¹ is the power.
-102.012 x is a monomial of degree 1 since x=x¹ is the power.
x²√5 is a monomial of degree 2 since x² is the power.
A polynomial is a sum of monomials.
e.g.
21x³ + 2x/3 + 5 is a polynomial.
x²√5 - 102.012 x is a polynomial.
21x³ + x²√5 + 2x/3 + 5 is a polynomial.
But:
21x³ is also a polynomial since it is also the sum of 21x³ and 0.x²
So every monomial is a polynomial.
The degree of a polynomial is the highest degree of all non-nil monomials it is the sum of:
e.g.
21x³ + 2x/3 + 5 is a polynomial of degree 3 since x³>x¹>xº
x²√5 - 102.012 x is a polynomial of degree 2 since x²>x¹
(25 - 5²)x³ + x² + 5 is a polynomial of degree 2 since x²>xº (the coefficient of x³ is nil!)
A quadratic is a polynomial of degree 2.
e.g
(25 - 5²)x³ + x² + 5 is a quadratic.
x²√5 - 102.012 x is a quadratic.
So a polynomial is not the same thing as a quadratic.
A quadratic is always a polynomial but a polynomial is not always a quadratic.
If you need an analogy:
A chihuahua is always a dog. But not all dogs are chihuahuas.
Explicatively,
Dragon.Jade :-)
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No. A polynomial is a function of a certain form (Google for "polynomial", read the Wikipedia link). A polynomial of degree 2 (see "degree" in the same Wikipedia article) is said to be quadratic. (You didn't really need someone to tell you to Google for the terms, did you?:)