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The polynomial function
f is defined as
f(c)=(c-k)(c^(2)-4c+4) where
k is a constant. The value 2 is a zero of
f. What is the remainder
f(c) when divided by
(c-2) ?

The polynomial function $f$ is defined as $f(c)=(c-k)\left(c^{2}-4 c+4\right)$ where $k$ is a constant. The value $2$ is a zero of $f$ . What is the remainder $f(c)$ when divided by $(c-2)$ ?

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Simplify radical expressions with variables

Full solution

Q. The polynomial function

f

is defined as

f(c)=(c-k)\left(c^{2}-4 c+4\right)

where

k

is a constant. The value

2

is a zero of

f

. What is the remainder

f(c)

when divided by

(c-2)

?

Plug $c=2$ : Since $2$ is a zero of $f$ , plug $c=2$ into the polynomial to find the remainder. $\newline$ $f(2) = (2-k)(2^2 - 4\cdot2 + 4)$
Simplify equation: Simplify the equation. $f(2) = (2-k)(4 - 8 + 4)$
Continue simplifying: Continue simplifying. $f(2) = (2-k)(0)$
Find remainder: Since anything multiplied by $0$ is $0$ , the remainder is $0$ . $\newline$ $f(2) = 0$

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