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

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