a Rewrite the terms in the form ax^b. If the expression is a polynomial, a can be any number and b must be a whole number.
B
b Simplify the expression by multiplying the parentheses.
C
c Where is the variable located in a polynomial expression?
D
d We can rewrite constants as ax^0.
E
e Simplify the expression by expanding the square.
F
f First isolate y by taking the square root of both sides.
G
g 1/a^b=a^(- b)
H
h Does a fraction fall under the definition any number?
I
i Rewrite the term in the form ax^b.
J
j We can rewrite constants as ax^0.
A
a Polynomial
B
b Polynomial
C
c Not a polynomial, see solution.
D
d Polynomial
E
e Polynomial
F
f Not a polynomial, see solution.
G
g Not a polynomial, see solution.
H
h Polynomial
I
i Polynomial
J
j Polynomial
Practice makes perfect
a Polynomials are expressions that can be written as a sum of terms of the form.
(any number)* x^((whole number))
Let's check if the terms follow the description of a polynomial.
( any number)* x^(( whole number))
↓
y= 3x^2+ 2x^2+ 1x^1
As we can see, the equation is a polynomial.
Now we can rewrite the terms and analyze the expression.
( any number)* x^(whole number)
↓
y= 1x^4- 6x^3+ 13x^2- 12x^1+ 4x^0
The equation is a polynomial.
c Examining the function, we notice that it contains a term that does not follow the description of a polynomial.
( any number)* x^(whole number)
↓
y= 1x^2+ 2^x
Therefore, this function is not a polynomial.
d Let's attempt to rewrite the terms so that they match the look of a polynomial.
( any number)* x^(whole number)
↓
y= 3x^1- 1x^0
This function is a polynomial.
e Before we can determine if this is a polynomial, we have to simplify it.
Having solved for y, we see immediately that the function does not match the look of a polynomial.
g Notice that an expression in the form 1a^b can be rewritten as a^(-b). With this information, we can rewrite the equation and determine if it is a polynomial.
( any number)* x^(whole number)
↓
y= 1x^(-2)+ 1x^(-1)+ 1/2x^0
As we can see, the function is not a polynomial.
h Again, let's rewrite the expression and try to match the terms with the look of a polynomial.
( any number)* x^(whole number)
↓
y= 1/2x^1+ 1/3x^0
The function is a polynomial.
i Again, let's rewrite the expression and try to match the terms with the look of a polynomial.
( any number)* x^(whole number)
↓
y= 1x^1
The function is a polynomial.
j Let's rewrite the expression and try to match the terms with the look of a polynomial.
( any number)* x^(whole number)
↓
y= - 7x^0
The function is a polynomial.
