*
Polynomial
- is an algebraic expression which has a finite sum terms. Each of term contains a product of a numerical coefficient and one or more variables raised to a power.
Useful Terms:
- is an algebraic expression which has a finite sum terms. Each of term contains a product of a numerical coefficient and one or more variables raised to a power.
Useful Terms:
1. Algebraic Expression
- collections of constant and variable which at least one operation in mathematics is applicable.
2. Variable
- Symbol that doesn't have a fixed value or constant.
- Symbol that doesn't have a fixed value or constant.
3. Constant
- has a fixed value.
- Maybe a symbol but still contains a certain value.
e.g. 3, 1/4, 𝜋, and G
- has a fixed value.
- Maybe a symbol but still contains a certain value.
e.g. 3, 1/4, 𝜋, and G
4. Term
- expression separated preceded by plus or minus sign.
e.g.
3x2, 4x, y, 5t (one term)
3x2 + 4x, 5t - y (two term) and so on . . .
- expression separated preceded by plus or minus sign.
e.g.
3x2, 4x, y, 5t (one term)
3x2 + 4x, 5t - y (two term) and so on . . .
5. Degree of
Polynomial
- exponent of variable.
e.g.
In the expression: 3x3 - 2x2 + 9x - 10
The highest degree is 3 from the term 3x3
- exponent of variable.
e.g.
In the expression: 3x3 - 2x2 + 9x - 10
The highest degree is 3 from the term 3x3
6. Monomial
- term which is a product of a real number and a variable whose integral exponent is a non-negative integral exponent.
- term which is a product of a real number and a variable whose integral exponent is a non-negative integral exponent.
e.g.
5x, 9x5 and 2x3 are all monomials while 1/5x, x + 2 and a/x are not.
5x, 9x5 and 2x3 are all monomials while 1/5x, x + 2 and a/x are not.
7. Binomial
- two terms separated by plus or minus sign which each is a product of a real number and a variable whose integral exponent is a non-negative integral exponent.
- two terms separated by plus or minus sign which each is a product of a real number and a variable whose integral exponent is a non-negative integral exponent.
* Operations of Polynomials
1. Addition
- Only terms having the same degrees and variables can be added.
- Degrees doesn't change, only their numerical coefficients.
e.g.
- Only terms having the same degrees and variables can be added.
- Degrees doesn't change, only their numerical coefficients.
e.g.
x2 + x
cannot be added because they don't have the same degree
x + 4y cannot be
added because they don't have the same variable
3x + 5x can be added because
they do have the same degree and variable
2. Subtraction
- have the same conditions with
Addition.
3. Multiplication
- Terms having different variables
or degrees can be multiplied.
- Numerical coefficients are multiplied but variable degrees or exponents are just added (Only if they are the same).
- Numerical coefficients are multiplied but variable degrees or exponents are just added (Only if they are the same).
e.g.
(3x)(5x3)
= 15x4
(7)(x2) = 7x2
(3x)(5y4) = 15xy4
(7)(x2) = 7x2
(3x)(5y4) = 15xy4
4. Division
- only terms or expression having the same variables can be divided.
- Degrees or exponent of variables are subtracted. (Numerator - Denominator)
- Numerical coefficient is divided normally.
- only terms or expression having the same variables can be divided.
- Degrees or exponent of variables are subtracted. (Numerator - Denominator)
- Numerical coefficient is divided normally.
e.g.
x3/x2 = x
15x5 / 3= 5x5
25x2/5x= 5x
