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djverab [1.8K]
2 years ago
13

Factor the polynomial and use the zeros to identify its graph. x4 − 5x3 − 20x2 + 60x + 144

Mathematics
1 answer:
Monica [59]2 years ago
5 0

The zeros of the polynomial are -3, -2, 4 and 6 and the graph of the polynomial is graph (a)

<h3>How to factor the polynomial?</h3>

The polynomial is given as:

P(x) = x^4 - 5x^3 - 20x^2 + 60x + 144

Expand the polynomial function

P(x) = x^4 - 10x^3 + 5x^3 + 24x^2 - 50x^2 + 6x^2 + 120x - 60x + 144

Rewrite the function as:

P(x) = x^4 - 10x^3 + 24x^2 + 5x^3 - 50x^2 + 120x + 6x^2 - 60x + 144

Factorize the function

P(x) = x^2(x^2 - 10x + 24) + 5x(x^2 - 10x + 24) + 6(x^2 - 10x + 24)

Factor out x^2 - 10x + 24

P(x) = (x^2 + 5x + 6)(x^2 - 10x + 24)

Expand each bracket

P(x) = (x^2 + 3x + 2x + 6)(x^2 - 4x - 6x + 24)

Factorize each bracket

P(x) = [x(x + 3) + 2(x + 3)][x(x - 6) - 4(x - 6)]

Factor out x + 3 and x - 6

P(x) = (x + 3)(x + 2)(x - 4)(x - 6)

Set to 0

(x + 3)(x + 2)(x - 4)(x - 6) = 0

Solve for x

x =-3, -2, 4 and 6

Hence, the zeros of the polynomial are -3, -2, 4 and 6 and the graph of the polynomial is graph (a)

Read more about polynomials at:

brainly.com/question/20896994

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nicole is flying two kites. she has 104 feet of string out to one kite and 110 feet out to the other kite. the angle formed by t
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48.49 feet

Step-by-step explanation:

The diagrammatic sketch of the information provided in the question was attached in the image below.

From the image below, the distance between the two kites is denoted by (c) and can be determined by using the cosine angle rule which is expressed as:

c^2 = a^2 + b^2 -2ab cos \ C

where;

a = 110

b = 104

Cos C = 26°

Then;

c^2 = 110^2 + 104^2 -2(110)(104) cos \ 26 \\ \\  c^2 = 12100 + 10816- 22880 ( 0.8988) \\ \\  c^2 = 22916- 20564.544 \\ \\  c^2 = 2351.456 \\ \\  c= \sqrt{2351.456} \\ \\ \mathbf{ c = 48.49 \ feet}

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1 on 7 is the answer!

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Read 2 more answers
Simplify the radical completely.
Sonja [21]

Answer:

D

Step-by-step explanation:

But basically, one by one you try moving the terms out of the radical.

75 is also 25 * 3 and since 25 has a perfect square root of 5 that goes out and 3 stays inside the radical.

x^3 is also x^2 * x and since x^2 has a perfect square root which is just x that goes outside while the remaining x stays inside.

y^9 is also y^8 * y and since we move variables out the radical in twos y^ goes outside the radical and y stays inside alone.

Finally, z is just z it can't be taken out so it stays inside the radical.

Hope that helps!

8 0
2 years ago
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