the polynomial `p(x)=x^(4)-2x^(3)+3x^(2)-ax+3a -7` when divided by x+1 leaves the remainder 19. find the values of A , also find the remainder when p(x) is divided by x+2.

Explanation

To solve the problem step-by-step, we will follow the instructions given in the video transcript and break down the calculations clearly.

### Step 1: Find the value of \( a \) using the Remainder Theorem

According to the Remainder Theorem, when a polynomial \( p(x) \) is divided by \( x + 1 \), the remainder can be found by evaluating \( p(-1) \). We know that this remainder is equal to 19.

Given the polynomial:
\[
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