Find k if (x+6) is a factor of the polynomial
f(x) = 2x4 + 9x3 – 17x2 + kx – 12k

The value of k is 2

Step-by-step explanation:

The polynomial remainder theorem

The polynomial remainder theorem states that the remainder of the division of a polynomial f(x) by (x-r) is equal to f(r).

The function:

has a factor of (x+6).

Applying the polynomial remainder theorem for r=-6, substitute x=-6

Operating:

If x+6 is a factor, then the remainder is zero:

36 -18k=0

Subtracting 36:

-18k=-36

k=-36 / (-18)=2

k=2

The value of k is 2

answer:

payment just for service  

→

$

87.12

payment for service including tax

→

$

94.09

explanation:

service only with 20% tip  

→

$

72.6

(

1

+

20

100

)

=

$

87.12

in the opening of the question the word 'service' is associated only with the pretax value.

the closing part of the question asks: how much did she pay for the  

service

−−−−−−  

so technically the answer is  

→

$

72.6

(

1

+

20

100

)

=

$

87.12

however, the intention of the question provider may have been that your answer is to be  

$

87.12

(

1

+

8

100

)

=

$

94.09

to 2 decimal places.

'

payment just for service  

→

$

87.12

payment for service including tax

→

$

94.09

tony b

mar 21, 2017

answer:

trying to explain it another way

explanation:

service charge  

.

→

$

72.60

20% tip  

20

100

×

$

72.60

=

$

14.52

−−−−−−  

←

add

$

87.12

tax  

8

100

×

$

87.12

=

$

6.97

−−−−−  

←

add

$

94.09

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