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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).

 Aug 8, 2021
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(not sure of this)

when   divided by (x-1)   r = 5      sub in x = 1

 

a (1^3) -6(1^2)+ b(1) - 5 = 5

a + b = 16      or   b = 16- a

 

when divided by (x-2)   r = - 53    sub in x = 2

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

8a + 2b = - 24                   sub in red equation for 'b'

 

8a + 2 ( 16-a) = - 24

6a = - 56

a = -9.333     then b = 16-a = 25.333      

 

Here is a graph I used to verify:

 

https://www.desmos.com/calculator/e2svzjdotb

 Aug 8, 2021

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