Question

is (x-2) a factor of f(x)= x³-8x²+14x-4? yes, (x-2) is a factor. the remainder is zero. no, (x-2) is not a factor. the remainder is zero. yes, (x-2) is a factor. there is a remainder. no, (x-2) is not a factor. there is a remainder.

Explanation:

Step1: Apply Factor Theorem

By Factor Theorem, if $(x-a)$ is a factor of $f(x)$, then $f(a)=0$. Here $a=2$, so calculate $f(2)$.

Step2: Compute $f(2)$

$$\begin{align*} f(2)&=2^3 - 8(2)^2 + 14(2) - 4\\ &=8 - 32 + 28 - 4\\ &=0 \end{align*}$$

Step3: Draw conclusion

Since $f(2)=0$, $(x-2)$ is a factor with remainder 0.

Answer:

A. Yes, (x-2) is a factor. The remainder is zero.