Polynomial reminders

Algebra Level 3

If the remainder of the polynomial x 3 − a x 2 + 47 x − b x^3-ax^2+47x-b when by x − 3 x-3 is 128 128 and when divided by x − 5 x-5 is 256 256 , what is the sum a + b a+b ?


The answer is 8.

ابراهيم فقرا by ابراهيم فقرا , 23, Israel

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1 solution

Otto Bretscher
Dec 29, 2018

We are told, cryptically, that f ( 3 ) = 128 f(3)=128 and f ( 5 ) = 256 f(5)=256 . Now solve a linear system in two unknowns to find that a = b = 4 a=b=4 . The answer is 8 \boxed{8} .

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