When a polynomial 2x^3+3x^2+ax+b is divided by (x-2) leaves remainder 2, and (x+2) leaves remainder -2.Find a and b.

p(x) = 2x³ + 3x² + ax + b when divided by x - 2 and x + 2 leaves the remainders 2 , - 2.

Value of a and b

✯ g(x) = x - 2

⟹ 0 = x - 2 [ g(x) = 0 ]

⟹ x = 2

★ p(2) = 2(2)³ + 3(2)² + a(2) + b

⟹ - 2 = 2 * 8 + 3 * 4 + 2a + b

⟹ - 2 - 16 - 12 - 2a = b

⟹ - 30 - 2a = b -- equation (1)

Similarly,

✯ g(x) = x + 2

⟹ 0 = x + 2

⟹ x = - 2

★ p( - 2) = 2( - 2)³ + 3( - 2)² + a ( - 2) + b

Substitute the value of b from equation (1).

⟹ 2 = 2 * ( - 8) + 3 * 4 - 2a - 30 - 2a

⟹ 2a + 2a = - 16 + 12 - 2 - 30

⟹ 4a = - 24

⟹ a = - 24/4

⟹ a = - 6

Substitute the value of a in equation (1).

⟹ - 30 - 2( - 6) = b

⟹ - 30 + 12 = b

⟹ - 18 = b

Therefore,

a = - 6

b = - 18.

I hope it will help you.

Regards.

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

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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

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$

72.60

=

$

14.52

−−−−−−  

←

add

$

87.12

tax  

8

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$

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related questions

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: