Which variable has the greatest exponent? This determines the polynomial's degree.
B
b
Notice that the x-term is non-existent, which can be interpreted as it having a coefficient of 0.
C
c
Notice that the constant is non-existent, which can be interpreted as it being 0.
D
d
First simplify the expression by multiplying the factors.
E
e
Rewrite the variable as 1x^1.
F
f
Rewrite the constant as 10x^0.
A
a
Fourth degree
a_4=6, a_3=- 3, a_2=5, a_1=1, a_0=8
B
b
Third degree
a_3=- 5, a_2=10, a_1=0, a_0=8
C
c
Second degree
a_2=- 1, a_1=1, a_0=0
D
d
Third degree
a_3=1, a_2=-8, a_1=15, a_0=0
E
e
First degree
a_1=1, a_0=0
F
f
Zero degree
a_0=10
Practice makes perfect
a
The degree of the polynomial is given by the variable with the greatest exponent. Examining the expression, we can identify this term.
6x^4-3x^3+5x^2+x+8
As we can see, this is a fourth degree polynomial. Finally, by rewriting some of the terms we can list the coefficients and label them.
6x^4+( - 3)x^3+ 5x^2+ 1x+ 8 [0.75em]
a_4= 6, a_3= - 3, a_2= 5,
a_1= 1, a_0= 8
b
Like in Part A, the degree of the polynomial is given by the variable with the greatest exponent. Examining the expression, we can identify this term.
- 5x^3+10x^2+8
As we can see, this is a third degree polynomial. Finally, by rewriting some of the terms, we can list the coefficients and label them. Notice that the x-term is non-existent, which can be interpreted as it having a coefficient of 0.
& - 5x^3+ 10x^2+ 0x^1+ 8 [0.75em]
& a_3= - 5, a_2= 10, a_1= 0, a_0= 8
c
Like in Parts A and B, we have to identify the variable with the greatest exponent. Examining the expression, we can identify this term.
- x^2+x
As we can see, this is a second degree polynomial. Finally, by rewriting some of the terms, we can list the coefficients and label them. Notice that the constant is non-existent, which can be interpreted as it being 0.
& - 1x^2+ 1x^1+ 0 [0.25em]
& a_2= - 1, a_1= 1, a_0= 0
d
Before we can determine the degree and coefficients, we have to simplify the expression.
Now we can determine the polynomial's degree.
x^3-8x^2+15x
This is a third degree polynomial. Finally, by rewriting some of the terms, we can list the coefficients and label them.
& 1x^3+( - 8)x^2+ 15x+ 0 [0.25em]
& a_3= 1, a_2= - 8, a_1= 15, a_0= 0
e
If we rewrite the expression, we see that this is a first degree polynomial.
x^1
Next, we will rewrite the expression and list the coefficients.
& 1x^1+ 0 [0.25em]
& a_1= 1, a_0= 0
f
If we rewrite the expression, we see that this is a zero degree polynomial.
10x^0
Finally, we will list the coefficients.
& 10 [0.25em]
& a_0= 10
