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Chapter 10 - Polynomials
Tab 1: Identifying Polynomials
Definition
Polynomials : Is a monomial or a sum ofmonomialsThe prefix poly- means more than one, the suffix –nomialmean name but in math it means terms.Therefore, Polynomial means more than oneterm.Examples of Polynomials: * Terms are separated by a +
or - sign.212x³y8x² + 4x – 3x² - 9
Identifying Polynomials
Polynomials are identified in two ways by the number of terms and by degree.
Identifying Polynomials by Terms
Monomial: Mon means one, a polynomial
with one term.
Examples of Monomials:-4x
5
6x²y³
Identifying Polynomials by Terms
* Terms are separated by a + or - sign.
• Binomial: Bi means two, a polynomial with two terms.Examples of Binomials:
-4x + 3
x³- 225
6x²y³ - x
Identifying Polynomials by Terms
* Terms are separated by a + or - sign. Trinomial: Tri means three, a polynomial
with three terms.Examples of Trinomials:
8x² + 4x – 3x²y³ + xy² – y64y³ + y² – 2
* More than 3 terms is called a polynomial*
Identifying Polynomials by Degree
Degree of the Polynomial is determined bythe largest exponent of the variable.Examples:
5x³ + 4x² -6 has a degree of 3 Cubicx² + 4 has a degree of 2 Quadratic3x + 1 has a degree of 1 Linear2 has a degree of 0
Constant
* More than a degree of 3 , just write the number.*
Let’s Put IT All Together
Polynomial Degree Identify by Degree
Identify by Terms
6
3x + 1
-x²+2x-5
4x³ - 8x
5x³+4x²-6x+14
Let’s Put IT All Together
Polynomial Degree Identify by Degree
Identify by Terms
6 0
3x + 1
-x²+2x-5
4x³ - 8x
5x³+4x²-6x+14
Let’s Put IT All Together
Polynomial Degree Identify by Degree
Identify by Terms
6 0 Constant
3x + 1
-x²+2x-5
4x³ - 8x
5x³+4x²-6x+14
Let’s Put IT All Together
Polynomial Degree Identify by Degree
Identify by Terms
6 0 Constant Monomial
3x + 1
-x²+2x-5
4x³ - 8x
5x³+4x²-6x+14
Let’s Put IT All Together
Polynomial Degree Identify by Degree
Identify by Terms
6 0 Constant Monomial
3x + 1 1
-x²+2x-5
4x³ - 8x
5x³+4x²-6x+14
Let’s Put IT All Together
Polynomial Degree Identify by Degree
Identify by Terms
6 0 Constant Monomial
3x + 1 1 Linear
-x²+2x-5
4x³ - 8x
5x³+4x²-6x+14
Let’s Put IT All Together
Polynomial Degree Identify by Degree
Identify by Terms
6 0 Constant Monomial
3x + 1 1 Linear Binomial
-x²+2x-5
4x³ - 8x
5x³+4x²-6x+14
Let’s Put IT All Together
Polynomial Degree Identify by Degree
Identify by Terms
6 0 Constant Monomial
3x + 1 1 Linear Binomial
-x²+2x-5 2
4x³ - 8x
5x³+4x²-6x+14
Let’s Put IT All Together
Polynomial Degree Identify by Degree
Identify by Terms
6 0 Constant Monomial
3x + 1 1 Linear Binomial
-x²+2x-5 2 Quadratic
4x³ - 8x
5x³+4x²-6x+14
Let’s Put IT All Together
Polynomial Degree Identify by Degree
Identify by Terms
6 0 Constant Monomial
3x + 1 1 Linear Binomial
-x²+2x-5 2 Quadratic Trinomial
4x³ - 8x
5x³+4x²-6x+14
Let’s Put IT All Together
Polynomial Degree Identify by Degree
Identify by Terms
6 0 Constant Monomial
3x + 1 1 Linear Binomial
-x²+2x-5 2 Quadratic Trinomial
4x³ - 8x 3
5x³+4x²-6x+14
Let’s Put IT All Together
Polynomial Degree Identify by Degree
Identify by Terms
6 0 Constant Monomial
3x + 1 1 Linear Binomial
-x²+2x-5 2 Quadratic Trinomial
4x³ - 8x 3 Cubic
5x³+4x²-6x+14
Let’s Put IT All Together
Polynomial Degree Identify by Degree
Identify by Terms
6 0 Constant Monomial
3x + 1 1 Linear Binomial
-x²+2x-5 2 Quadratic Trinomial
4x³ - 8x 3 Cubic Binomial
5x³+4x²-6x+14
Let’s Put IT All Together
Polynomial Degree Identify by Degree
Identify by Terms
6 0 Constant Monomial
3x + 1 1 Linear Binomial
-x²+2x-5 2 Quadratic Trinomial
4x³ - 8x 3 Cubic Binomial
5x³+4x²-6x+14 3
Let’s Put IT All Together
Polynomial Degree Identify by Degree
Identify by Terms
6 0 Constant Monomial
3x + 1 1 Linear Binomial
-x²+2x-5 2 Quadratic Trinomial
4x³ - 8x 3 Cubic Binomial
5x³+4x²-6x+14 3 Cubic
Let’s Put IT All Together
Polynomial Degree Identify by Degree
Identify by Terms
6 0 Constant Monomial
3x + 1 1 Linear Binomial
-x²+2x-5 2 Quadratic Trinomial
4x³ - 8x 3 Cubic Binomial
5x³+4x²-6x+14 3 Cubic Polynomial