$P(x)$ is a polynomial with real coefficients such that $P(2+i)=4-3i$. There is a linear function $Q(x)=ax+b$ with real coefficients such that $Q(2+i)=P(2+i)$. Find $Q(x)$.

Q(2+i) = a(2+i) + b = 2a+b + ai

Since Q(2+i) = P(2+i) we must have 2a+b + bi = 4 - 3i

Equate real and imaginary parts Real: 2a + b = 4

Imag: b = -3

I'll leave you to finish this.