When a polynomial $p(x)$ is divided by $x + 1,$ the remainder is 5.  When $p(x)$ is divided by $x + 5,$ the remainder is $-7.$  Find the remainder when $p(x)$ is divided by $(x + 1)(x + 5).$
Question:
When a polynomial $p(x)$ is divided by $x + 1,$ the remainder is 5.  When $p(x)$ is divided by $x + 5,$ the remainder is $-7.$  Find the remainder when $p(x)$ is divided by $(x + 1)(x + 5).$
Answer:
Let's think step by step.

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3x + 8
When a polynomial $p(x)$ is divided by $x + 1,$ the remainder is 5.  When $p(x)$ is divided by $x + 5,$ the remainder is $-7.$  Find the remainder when $p(x)$ is divided by $(x + 1)(x + 5).$
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