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use the remainder theorem to find the remainder when f(x) is divided by x-1. then use the factor theorem to determine whether x-1 is a factor of f(x).

f(x)=4x^{3}-7x^{2} -2x+6

find the remainder:

see explanation

Step-by-step explanation:

The Remainder theorem states that if f(x) is divided by (x - h) then

f(h) is the remainder, thus

division by (x - 1) then h = 1

f(1) = 4(1)³ - 7(1)² - 2(1) + 6

     = 4 - 7 - 2 + 6 = 1 ← remainder

The factor theorem states that if (x - h) is a factor of f(x), then f(h) = 0

Here f(1) = 1

Hence (x - 1) is not a factor of f(x)