e The degree needs to be at least as high as the number of solutions.
A
a See solution.
B
b See solution.
C
c See solution.
D
d See solution.
E
e Part A → Lowest degree is 5
Part B → Lowest degree is 5
Part C → Lowest degree is 4
Part D → Lowest degree is 6
Practice makes perfect
a A graph that has 5 real solutions reflects a fifth degree polynomial that intercepts the x-axis 5 times. We see an example of this below.
b In this case we are still dealing with a fifth degree polynomial, because we have five solutions in total. However, 3 are real and 2 are complex, which means it should only intercept the x-axis three times. We see an example of this below.
c A graph that has 4 complex solutions reflects a fourth degree polynomial that does not intercept the x-axis. Since it is a fourth degree polynomial, it changes direction three times. We see an example of this below.
d A graph that has 4 complex solutions and 2 real solutions has a total of 6 roots. This means the function is a sixth degree polynomial that intercepts the x-axis twice. We see an example of this below.
e The degree needs to be at least as high as the number of solutions. With this information, we can determine the lowest degree.
Part A& → lowest degree is 5
Part B& → lowest degree is 5
Part C& → lowest degree is 4
Part D& → lowest degree is 6
