A1. Suppose $x$ is a real number such that $x(x+3)=154$. Determine the value of $(x+1)(x+2)$.
Solution 1: The answer is 156 .
Expanding $x(x+3)=154$ yields $x^{2}+3 x=154$.
Hence, $(x+1)(x+2)=x^{2}+3 x+2=154+2=156$.
Solution 2: The answer is 156 .
$154=11 \times 14=(-11) \times(-14)$. In the former case $x=11$ and $12 \times 13=156$. In the latter case $x=-14$ and $(-13) \times(-12)=156$.