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