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First of all question is 84 not 8 in p(x),
x² + x - 12 divides f(x) = x³ + ax² + bx - 84 exactly find a and b.
The equation x² + x - 12 divides the equation x³ + ax² + bx - 84 exactly.
Since, reminder = 0
On Dividing, the given equation by x² + x - 12, we get
(a - 8)x² + (b + 5)x = 0
by comparision,
a = 8 and b = -5
Hence, the values of a and b are 8 and -5.
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