Use synthetic division and the Remainder Theorem to find P(a).
1. P(x) = 6x^4 + 19x^3 - 2x^2 - 44x - 24; a = -2/3
2. P(x) = x^3 + 3x^2 - 5x - 4; a = -1
1. Synthetic Division:
\begin{array}{ccccccc}
& & & & & & 6 \\
& & & & & -2/3 & 19 \\
& & & & -2/3 & -4 & -2 \\
& & & -2/3 & -7 & -44 & -24 \\
& & -2/3 & -9 & -48 & 0 & P(-2/3) \\
\end{array}
P(-2/3) = -48
2. Synthetic Division:
\begin{array}{ccccccc}
& & & & & & 1 \\
& & & & & -1 & 3 \\
& & & & -1 & -2 & -5 \\
& & & -1 & -3 & -7 & -4 \\
& & -1 & -4 & -10 & 0 & P(-1) \\
\end{array}
P(-1) = -10