find the remainder when x cube - ax square + 6x - a is divisible by x-a
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Answer:
5a
Step-by-step explanation:
Let p(x) be any polynomial of degree greater than or equal to one and let 'a' be any real number. If a polynomial p(x) is divided by x - a then the remainder is p(a).
Let p(x) = x3 - ax2 + 6x - a
The root of x - a = 0 is a.
p(a) = (a)3 - a(a)2 + 6(a) - a
= a3 - a3 + 5a
= 5a
Hence by remainder theorem, 5a is the remainder when x3 - ax2 + 6x - a is divided by x - a.
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