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Find the ordered pair \((a, b)\) of real numbers for which \((ax + b)(x^5 + 1) - (5x + 1)\)
is divisible by \(x^2+1.\)

 Mar 24, 2020
 #1
avatar+2854 
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Now, the beggar stands before me. His head bowed, his hands open, surrendered. What is the difference between me and the beggar? Two different worlds, two different minds, two different personalities. Why is he the beggar, but not me? The ragged clothes, the dirtied hands, what has he done to deserve this fate?


Now in my hands is the beggar's life. My choice, his life. I am the one to decide his fate. 

 

Now the beggar is shaking, sweating. The deadline is approaching. He is in need of help, and here I am in my bed at 11:30 with a sleep deprived brain.

 

Now I am tired. He is not. The adrenaline fueled desperation has given him the natural energy of the mind. A psychological energy. A willing to do whatever it takes to survive. Does he though? Does he have the will? Is it just animal instinct?

 

Now I look upon the beggar. He stretches his arms as far as he can. as far as he ever did in his life. His hands open wide, the bones cracking with the tension.

 

"Ha! What a noob! What am I to recieve in return for my effort and offfering?" I ask.

 

"Gratitude." Answered the beggar.

 

Now I pondered this for a second, then replied:

 

"Will this Gratitude change my life? Will it even EFFECT me? Your ripples of Gratitude in this universe are insignificant. So insignificant they are non-existant."

 

"Plez. Or else I will give you Coronavirus"

 

"You DARE threaten me? A beggar DARES threaten me?"

 

"Plez plez plez my homework is due really soon"

 

"Pffft. I will not help you." I scoffed as I walked away.

 

 

Now, the beggar awaits a good samaritan.

 Mar 24, 2020
 #2
avatar+24995 
+2

Find the ordered pair (a, b) of real numbers for which
\((ax + b)(x^5 + 1) - (5x + 1)\)
is divisible by \(x^{2}+1\).

 

answer see: https://web2.0calc.com/questions/more-polynomial-help-thanks#r4

 

laugh

 Mar 24, 2020

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