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Find the values of a and b so that 2x^(3...

Find the values of a and b so that `2x^(3)+ax^(2)+bx-14` has (x-1) and (x+2) are its factors.

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To find the values of \( a \) and \( b \) such that the polynomial \( 2x^3 + ax^2 + bx - 14 \) has \( (x-1) \) and \( (x+2) \) as its factors, we can follow these steps: ### Step 1: Set up the polynomial Let \( P(x) = 2x^3 + ax^2 + bx - 14 \). ### Step 2: Use the factor theorem Since \( (x-1) \) is a factor, we have: \[ P(1) = 0 \] ...
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