Find the equation of the line passing through the points (0; 2) and (1; 5)
2 answers:
You might be interested in
Answer:
Part 1)
The possible multiplicities are:
multiplicity 1
multiplicity 3
multiplicity 1
multiplicity 2
Part 2
The factored form is
Step-by-step explanation:
Part 1.
The missing diagram is shown in the attachment.
The zeroes of the seventh degree polynomial are the x-intercepts of the graph.
From the graph, we have x-intercepts at:
,
,
, and
.
The multiplicities tell us how many times a root repeats.
Also, even multiplicities will not cross their x-intercept, while odd multiplicities cross their x-intercepts.
The possible multiplicities are:
multiplicity 1
multiplicity 3
multiplicity 1
multiplicity 2
Note that the total multiplicity must equate the degree.
Part 2)
According to the factor theorem, if is a zero of p(x), then
is a factor.
Using the multiplicities , we can write the factors as:
Therefore the completely factored form of this seventh degree polynomial is
