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If the polynomial x^(3)+ax^(2)-bx-30 is...

If the polynomial `x^(3)+ax^(2)-bx-30` is exactly divisible by `x^(2)-2x-15`. Find a and b and also the third factor.

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To solve the problem, we need to find the values of \( a \) and \( b \) such that the polynomial \( x^3 + ax^2 - bx - 30 \) is exactly divisible by \( x^2 - 2x - 15 \). ### Step 1: Factor the divisor First, we will factor the quadratic polynomial \( x^2 - 2x - 15 \). \[ x^2 - 2x - 15 = (x - 5)(x + 3) \] ...
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