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3 years ago

Plz help me, URGENT!! 15 points!

Mathematics

1 answer:

bulgar [2K]3 years ago

5 0

Answer:

i just neeed the points

Step-by-step explanation:

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4 years ago

HELPPP ASAPPP!! 50 POINTS!!!

OleMash [197]

Answer:

Part 1)

The possible multiplicities are:

$x=-7$ multiplicity 1

$x=-3$ multiplicity 3

$x=2$ multiplicity 1

$x=5$ multiplicity 2

Part 2

The factored form is

$p(x)=(x+7)(x+3)^3(x-2)(x-5)^2$

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:

$x=-7$ , $x=-3$ , $x=2$ , and $x=5$ .

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:

$x=-7$ multiplicity 1

$x=-3$ multiplicity 3

$x=2$ multiplicity 1

$x=5$ multiplicity 2

Note that the total multiplicity must equate the degree.

Part 2)

According to the factor theorem, if $x=a$ is a zero of p(x), then $(x-a)$ is a factor.

Using the multiplicities , we can write the factors as:

$x+7$

$(x+3)^3$

$(x-2)^1$

$(x-5)^2$

Therefore the completely factored form of this seventh degree polynomial is $p(x)=(x+7)(x+3)^3(x-2)(x-5)^2$

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4 years ago