turkey-yks 2025 Q12

turkey-yks · Other · yks-ayt Factor & Remainder Theorem Polynomial Construction from Root/Value Conditions

Let $P(x)$ and $Q(x)$ be polynomials with real coefficients such that $P(x) + Q(x)$ is a second-degree polynomial and
$$\begin{aligned} & P(x) \cdot Q(x) = -4 \cdot (x-1)^{4} \cdot (x-2)^{2} \\ & P(3) = -16 \end{aligned}$$
are satisfied. Accordingly, what is the value of $Q(4)$?
A) 12 B) 24 C) 36 D) 48 E) 54

Let $P(x)$ and $Q(x)$ be polynomials with real coefficients such that $P(x) + Q(x)$ is a second-degree polynomial and

$$\begin{aligned}
& P(x) \cdot Q(x) = -4 \cdot (x-1)^{4} \cdot (x-2)^{2} \\
& P(3) = -16
\end{aligned}$$

are satisfied.
Accordingly, what is the value of $Q(4)$?

A) 12
B) 24
C) 36
D) 48
E) 54

Paper Questions

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