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Snowcat [4.5K]
3 years ago
15

YOur math teacher gives you a worksheet that has 20 problems. She tells you choose 3/4 of the problems can you skip? If you get

one third of the assigned problems done in class, how many problems do you have for homework?
Mathematics
1 answer:
sergiy2304 [10]3 years ago
3 0

Answer:

Step-by-step explanation:

mholwalker16

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Answer:

The factor form of given expression is (x-4)(x-2i)(x+2i).

Step-by-step explanation:

The given expression is

x^3-4x^2+4x-16

It can be written as

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According to the rational root theorem, all possible rational roots are in the form of

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Where, a₀ is constant term and a_n is leading coefficient.

f(4)=4^3-4(4)^2+4(4)-16=0

Since the value of f(x) is 0 at x=4, therefore 4 is a root of the function and (x-4) is a factor of given expression.

Use synthetic method to find the remaining factors.

(x^3-4x^2+4x-16)=(x-4)(x^2+4)

(x^3-4x^2+4x-16)=(x-4)(x^2-(2i)^2)

(x^3-4x^2+4x-16)=(x-4)(x-2i)(x+2i)

Therefore the factor form of given expression is (x-4)(x-2i)(x+2i).

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