1. Polynomial Vocabulary
Algebra 1
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2. A number, a variable or the product of numbers and variables.
Monomial
A number, a variable or the product of numbers and variables.
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3. Monomial Examples: 10 x x2 7xy 6 Is a monomial? Is 504.1 a monomial?
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4. An expression that can be written as the SUM of 2 monomials.
Binomial
An expression that can be written as the SUM of 2 monomials.
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5. Binomial Examples: 4 + 2x 10x + - 2 x2 – 5x xy + ⅝ Is a binomial?
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6. An expression that can be written as the SUM of 3 monomials.
Trinomial
An expression that can be written as the SUM of 3 monomials.
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7. Trinomial
Examples:
x3 + x2 – 5
x5 – x + ⅞
x10 – 5x + 1
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8. An expression that can be written
Polynomial
An expression that can be written
as a monomial or
the sum of monomials.
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9. Polynomial
Examples: 2x4 – 2 x5 – 5y + x2 4 x5 – 5 + x2 - x3 – 5x + xy Is this a polynomial? 8x
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10. Standard Form of a Polynomial
Standard Form of a polynomial is when you write the polynomial from largest exponent to smallest on the variable.
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11. Standard Form of a Polynomial
Examples of polynomials written in standard form:
x10 – 5x2
7x5 + x2 + 5
x5 – 5x4 + 7x3 + x2 + x - 3
Write 4x2 – x6 + 7x3 in standard form.
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12. Leading Coefficient
The coefficient of the term with the highest exponent.
When written in standard form, the leading coefficient is the first coefficient.
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13. Leading Coefficient Identify the leading coefficient.
a) 7x10 – 5x l.c. =
b) 3x2 + x l.c. =
c) 18 – 10x l.c. =
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14. Degree of Standard Form
The degree of a polynomial is the largest exponent of the variables when converted to
standard form.
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15. Degree of a Polynomial in Standard Form
Identify the degree of each polynomial. a) x8 – 5 + 5x2 has degree ... b) Quadratic Functions are degree… c) Linear Functions are degree… d) 9 has degree 9 is the same as 9x0
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16. Factored Form Polynomials may also be written in factored form.
Factored form looks like…..
(Polynomial)*(Polynomial)*...*(Polynomial)
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17. Factored Form Examples of Factored Form: (x + 4)(3x – 1)
5x(x + 12)3(x + 7)(x – 3)
(x3 + 4)(3x2 – 5)(x + 1)2
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18. Degree of Factored Form
When a polynomial is written in factored form, the degree can be determined by the number of x terms being multiplied together.
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19. Identify the degree of each polynomial in factored form
a) (x + 4)(3x – 1) Deg =
b) 8(x – 4)(x2 + 12)(x + 7)(x – 2) Deg =
c) x2(x + 8) Deg =
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20. Each monomial is called a term.
Terms of a polynomial
Each monomial is called a term.
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21. Terms of a polynomial Identify the number of terms.
a) x5 – 5 + x # of terms =
b) x2 # of terms =
c) 6x4 – 5 + x2 + x5 + x8 # of terms =
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22. The End
Clap your hands and whistle!
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