Define \( T: P_2 \to \mathbb{R}^2 \) by \[ T(p) = \begin{bmatrix} p(4) \\ p(6) \end{bmatrix}. \] Find a non-trivial element of the kernel. \[ p(t) = \underline{\hspace{3cm}} \]

f(x) Let f(x) = 16x5 – 48x – 8x³ and g(x) = 8x?. Find g(x) O 2x2 + 6x + 1 O 2x2 - 6x - 1 O 2x3 + 6x2 + x O 2x3 – 6x2 – x

a. Evaluate f(6) given that x² + (12 – 5x) f(x) 8x f(6) = 3/8 Preview b. Evaluate g(x + 2) given that g(x) = 4x² – 6x + 8. g(x + 2) = Preview y3 4 c. Evaluate h(2x) given that h(y) 7y h(2x) = Preview

Consider the polynomial p(x) = 2 (x + 1) (x – 3)² (A) As х — —с0 y →? (В) As y →? (C) Find the zeros and their multiplicities.