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if x²+x-12 divides completely the polynomial x³+ax²+bx-84 then find the value of a and b

$w e a r e g i v e n t h a t, x^{2} + x - 12 d i v i d e s x^{3} + a x^{2} + b x - 84 s o, w e m a y s a y t h a t, x^{3} + a x^{2} + b x - 84 = (x^{2} + x - 12) (x + p) \Rightarrow x^{3} + a x^{2} + b x - 84 = x^{3} + x^{2} - 12 x + p x^{2} + p x - 12 p \Rightarrow x^{3} + a x^{2} + b x - 84 = x^{3} + (1 + p) x^{2} + (p - 12) x - 12 p n o w, o n e q u a t i n g t h e c o - e f f i c i e n t s, w e g e t 1 + p = a p + 12 = b - 12 p = - 84 \Rightarrow p = 7 s o, a = 1 + p = 8 a n d, b = - 12 + p = - 5 h e n c e, a = 8 b = - 5 s o, x^{2} + x - 12 d i v i d e s x^{3} + 8 x^{2} - 5 x - 84$

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