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When f(x) = ax^3 - 6x^2 + bx - 5 is divided by x - 1, the remainder is 5. When f(x) is divided by x - 2, the remainder is -53. Find the ordered pair (a,b).

 Jun 29, 2021
 #1
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Sub in x = 1

 

a - 6 + b -5 = 5 

a+b - 16 = 0    (1)

 

sub in x = 2

 

8a - 24 + 2b -5 = -53

8a +2b +24 = 0        (2)

 

Two equations with two unknowns   solve for a and b

mutilpy (1) by -8

-8a-8b+128 = 0    add to (2)

-6b +152 = 0

b = 25 1/3      a= - 9 1/3

 Jun 29, 2021

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