\text{Part B } \rightarrow 4^\text{th} degree
\text{Part C } \rightarrow 3^\text{rd} degree
Practice makes perfect
a
Let's calculate the corresponding y-values for the given x-values. We will only be substituting integers for x.
x
(x-1)^2(x+1)
y
-2
( -2-1)^2( -2+1)
-9
-1
( -1-1)^2( -1+1)
0
0
( 0-1)^2( 0+1)
1
1
( 1-1)^2( 1+1)
0
2
( 2-1)^2( 2+1)
3
Let's simplify our table.
x
y
- 2
- 9
- 1
0
0
1
1
0
2
3
Finally, we will plot the points in a coordinate plane and draw the graph.
b
Let's calculate the corresponding y-values for the given x-values.
x
(x-1)^2(x+1)^2
y
-2
( -2-1)^2( -2+1)^2
9
-1
( -1-1)^2( -1+1)^2
0
0
( 0-1)^2( 0+1)^2
1
1
( 1-1)^2( 1+1)^2
0
2
( 2-1)^2( 2+1)^2
9
Let's simplify our table.
x
y
- 2
9
- 1
0
0
1
1
0
2
9
Finally, we will plot the points in a coordinate plane and draw the graph.
c
Let's calculate the corresponding y-values for the given x-values.
x
x^3-4x
y
-2
( -2)^3-4( -2)
0
-1
( -1)^3-4( -1)
3
0
( 0)^3-4( 0)
0
1
( 1)^3-4( 1)
-3
2
( 2)^3-4( 2)
0
Let's simplify our table.
x
y
- 2
0
- 1
3
0
0
1
- 3
2
0
Finally, we will plot the points in a coordinate plane and draw the graph.
d
In order to tell the degree of each of the polynomials from Parts A to C, we should first write them in standard form.
y=a_n x^n + a_(n-1)x^(n-1) + ⋯ + a_1 x^1 + a_0x^0
Notice that the function from Part C is already written in standard form. This means that we can identify the degree by finding the highest power to which x is raised.
c. y=x^3-4x
The polynomial from Part C has a degree of 3. Let's move on to the polynomials from Parts A and B, which require us to rewrite them in standard form. We will start with Part A.
Looking at the rewritten polynomial, we can see that the largest power that x is raised to is 3. This means that it is also a {\color{#FF0000}{3}}^\text{rd} degree polynomial.
a. y=x^3-x^2-x+1
Finally, let's rewrite the polynomial from Part B in standard form.
