Question

determine if ((x - 1)) is a factor of (5x^4 - 2x^3 + 3x - 6).
yes
no

Explanation:

Step1: Apply Factor Theorem

Use $f(1)$ to test divisibility.

Step2: Substitute $x=1$ into polynomial

$$f(1)=5(1)^4 - 2(1)^3 + 3(1) - 6$$

Step3: Calculate each term

$$f(1)=5 - 2 + 3 - 6$$

Step4: Compute final value

$$f(1)=0$$
Since $f(1)=0$, $(x-1)$ is a factor.

Answer:

Yes