Basics of Polynomials

The basics on polynomials,definitions, simplifying and polynomial functions.

What are terms? (def)

Mathamatical expressions made up of 2 different parts.

What are the 2 parts that make up a term?

A number and a variable

What are terms? (def)

Mathamatical expressions made up of 2 different parts.

What are the 2 parts that make up a term?

A number and a variable

Which way do you organize a term?

1x or x1

1x (number then term)

What are number parts in a term called?

coefficents

What is a polynomial? (def)

A series of terms joined together with + or -

what are variable parts? (def)

One or more variables raised to a power

Is this a term?

6x²

yes

Is this a term?

88²

no

What do you call a polynomial with one term?

A mononomial

What do you call a polynomial with two terms?

A binomial

What do you call a polynomial with three terms?

A trinomial

What do you call an expression with 4 or more terms?

A polynomial

x+4x²-5

Convert this equation so that it maintains the same value but it becomes a trinomial.

1x¹+4x²-5x⁰

What is x⁰ ? And why would you add it to an equation?

x⁰=1 You would add it when trying to form a term with a number that doesn’t have a variable part

Is this a term?

5x

yes

Why is 3 not a term and what do you need to add for it to become a term?

3 is not a term because there is no variable. To convert it to a term make it 3×⁰

simplify 2x²+1x¹-5x⁰

2x²+x-5

If you were simplyfying a polynomial which would come first? x or 2?

x=x¹ 2=2x⁰

x would come first.

What is a constant term?

A term with a value that always stays the same.

What is the constant term in the equation;

8x²+x-8

-8 is the constant term

-8=-8x⁰ -8x⁰=-8

How do you find the degree of a term?

The degree of a term is determined by the power of the variable part

what degree term is 6x² ?

a second degree term

What degree term is 55g⁷ ?

a 7th degree term

What degree term is 5x⁰

[A 0th degree term]: a constant term

Is 8x³z⁹ a term?

yes

What degree term is 6j²r⁴

a fourth degree term

Is this a polynomial 5x⁻³

no

Can a polynomial have negative exponent or degree?

NO

How do you find the degree of a polynomial?

By finding the highest degree term

What degree is this polynomial?

7x⁴+2y²

4th degree polynomial

What degree is this polynomial?

68g³-50x⁵

5th degree polynomial

How do you arrange a polynomial?

From highest degree to lowest degree

Rearrange this polynomial.

8z¹-5x⁷+2j³-6g⁹

-6g⁹-5x⁷+2j³+8z¹

Rearrange this polynomial

4y⁵+8-10x

4y⁵-10x+8

How would you make x into a term?

1x¹

Simplify this polynomial

1x³+1x³

2x³

What are like terms?

Terms with the same variable part

are 3x² and 3x⁴ like terms?

no because the variable has to be raised to the same power.

are 4x³ and 7x³ like terms?

yes, so you can combine them into 11x³

What is this process called?

combining like terms

Are 4x and 55x like terms?

yes, so you can combine them into 59x

Are 2x² and -7x² like terms?

yes, so you can combine them into -5x²

Are -5yx and 8xy like terms?

yes because yx=xy

Are 5x²y and 5y²x like terms?

No because x²y≠y²x

What is a leading coefficient?

The number part in the highest degree term [in a polynomial]

What is the leading coefficient in 8x²-2x⁵+x

-2

What is the leading coefficient in 8+x⁴-5+7x²

1

What is the leading coefficient in 7x⁹-78+x+x³

7x⁹

In a polynomial, ____ have to be whole and positive intergers

exponents

Is this a polynomial function?

g(x) = x² - 4x + 7/x = x² - 4x + 7x^-1

No, there is a negative exponent

Is this a polynomial function?

f(x) = x² - 4x + 7

yes

A polynomial function cannot equal ____

zero

Is this a Polynomial function?

f(x)=9

Yes, it can be represented as; f(x)= 9x⁰

Is this a polynomial function?

f(x)= 4x^½

No, the exponent has to be a whole number

is this a polynomial function?

f(x)=0

No, a polynomial function cannot equal zero

Is this a polynomial function?

f(x)=7x⁹+5x²-x+3

Yes

What type of polynomial is this?

1x²

A monomial

What type of polynomial is this?

9x²+17y⁸+18z³

A trinomial

What type of polynomial is this?

34g⁸+80y⁴g⁵

A binomial

What do you call a 1st degree polynomial equation?

Linear equation

What do you call a 2nd degree polynomial equation?

quadratic equation

What do you call a 3rd degree polynomial equation?

Cubic equation

What do you call a 4th degree polynomial equation?