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use the remainder theorem to find the remainder when f(x) is divided by x-2. then use the factor theorem to divide x-2 is a factor of f(x).
f(x)=4x^4-7x^3-5x+2

the remainder is ?

is x-2 a remainder of f(x)=4x^4-7x^3-5x+2

is x-2 a factor of f(x) .... ?

f(2) = 4(2^4) - 7(2^3) - 5(2) + 2
= 64 - 56 - 10 + 2 = 0

yes, x-2 is a factor.

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