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

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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.

To find the remainder when dividing f(x) by x-2 using the remainder theorem, follow these steps:

1. Replace x in f(x) with the divisor, which is 2:
f(2) = 4(2)^4 - 7(2)^3 - 5(2) + 2

2. Simplify the expression:
f(2) = 4(16) - 7(8) - 10 + 2
= 64 - 56 - 10 + 2
= 0

Therefore, the remainder when f(x) is divided by x-2 is 0.

To determine if x-2 is a factor of f(x), you can use the factor theorem. If the remainder is 0 when f(x) is divided by x-2, then x-2 is a factor of f(x). Since the remainder we found was 0, we can conclude that x-2 is indeed a factor of f(x).