Question

p(x) = x⁴ - 2x³ + kx - 4, where k is an unknown integer. p(x) divided by (x - 1) has a remainder of 0. what is the value of k?

Explanation:

Step1: Apply Remainder Theorem

If $p(x)$ divided by $(x-1)$ has remainder 0, then $p(1)=0$.

Step2: Substitute $x=1$ into $p(x)$

$$p(1) = 1^4 - 2(1)^3 + k(1) - 4$$

Step3: Simplify the expression

$$p(1) = 1 - 2 + k - 4$$
$$p(1) = k - 5$$

Step4: Set equal to 0 and solve for $k$

$$k - 5 = 0$$
$$k=5$$

Answer:

$k=5$