Find the reminder when $x^3-bx^2+6x-b$is divided by $x-b$

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Find the reminder when $x^3-bx^2+6x-b$ is divided by $x-b$

A $b^2 + 4$

B5b

C2b - 3

D3b + 6

Answer:

when a polynomial p(x) is divided by (x - a) for some number a , the reminder r = p(a)

When p(a) = 0 then (x -a) is a factor of p(x)

$p(x)=x^3-bx^2+6x-b$

$x-b=0\implies{x=b}$

$p(b)=b^3-b\times{b^2}+6b-b$

$=b^3-b^3+6b-b$

$=5b$

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