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Use the remainder theorem to find the remainder when P(x) is divided

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use the remainder theorem to find the remainder when P(x)
is divided by x-c. Is x-c a factor of P(x)? if so write in
factored form
P(x)=x^6-16x^4+x^2-16; x+4
Solution
when P(x) is divided by x-c, the remainder
obtained is P(c) so, for P(x)=x^6-16x^4+x^2-16, x+4 c=-4
P(-4)=4^6-16*6^4+4^2-16=0 so, x+4 divides P(x) P(x)=
x^4(x^2-16)+ x^2-16 =(x^2-16)(x^4+1) =(x-4)(x+4)(x^4+1)

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use the remainder theorem to find the remainder when P(x) is divided by x-c. Is x-c a factor of P(x)? if so write in factored form P(x)=x^6-16x^4+x^2-16; x+4 Solution when P(x) is divided by x-c, the remainder obtained is P(c) so, for P(x)=x^6 -16x^4+x^2-16, x+4 c=-4 P(-4)=4^6-16*6^4+4^2-16=0 so, ...
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