Write the function in factored form, and give all the possible rational zeros of the function.
f(x) = x^4 − x^3 + 7x^2 − 9x

Question

Write the function in factored form, and give all the possible rational zeros of the function.
f(x) = x^4 − x^3 + 7x^2 − 9x − 18

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Serenity 2 months 2021-08-06T08:58:56+00:00 1 Answers 0 views 0

Answers ( )

    0
    2021-08-06T09:00:42+00:00

    Answer:

    Step-by-step explanation:Explanation:

    First notice that by reversing the signs of the coefficients of the terms with odd degree, the sum is zero. So  

    x

    =


    1

    is a zero:


    f

    (


    1

    )

    =

    1

    +

    1

    +

    7

    +

    9


    18

    =

    0


    and  

    (

    x

    +

    1

    )

    is a factor:


    x

    4


    x

    3

    +

    7

    x

    2


    9

    x


    18


    =

    (

    x

    +

    1

    )

    (

    x

    3


    2

    x

    2

    +

    9

    x


    18

    )


    then factor by grouping…


    =

    (

    x

    +

    1

    )

    (

    (

    x

    3


    2

    x

    2

    )

    +

    (

    9

    x


    18

    )

    )


    =

    (

    x

    +

    1

    )

    (

    x

    2

    (

    x


    2

    )

    +

    9

    (

    x


    2

    )

    )


    =

    (

    x

    +

    1

    )

    (

    x

    2

    +

    9

    )

    (

    x


    2

    )


    then take square root of  


    9

    to find:


    =

    (

    x

    +

    1

    )

    (

    x


    3

    i

    )

    (

    x

    +

    3

    i

    )

    (

    x


    2

    )


    So the zeros are  

    x

    =


    1

    ,  

    x

    =

    3

    i

    ,  

    x

    =


    3

    i

    and  

    x

    =

    2

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