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If a^(2)-2a-3 is a factor of a^(4)+pa^(3...

If `a^(2)-2a-3` is a factor of `a^(4)+pa^(3) +qa^2+12a-9`, find the value of `p^(2)-2q-3`.

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To solve the problem, we need to find the values of \( p \) and \( q \) such that \( a^2 - 2a - 3 \) is a factor of \( a^4 + pa^3 + qa^2 + 12a - 9 \). ### Step-by-step Solution: 1. **Factor the Quadratic Polynomial**: We start by factoring the polynomial \( a^2 - 2a - 3 \): \[ a^2 - 2a - 3 = (a - 3)(a + 1) ...
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