Asked by HELP HELP HELP MNHS

If (x+3)(x-2)(x+1)=(x+2)Q(x)+(x+3)(x-2)

(with solution pls... thanks)
Answered by Reiny
I will assume we solving for Q(x)
let a = Q(x) for easier typing

(x+3)(x-2)(x+1) - (x+3)(x-2) = (x+2)a
(x+2)a = (x+3)(x-2)[x+1 - 1]
a = x(x+3)(x-2)/(x+2)

Q(x) = x(x+3)(x-2)/(x+2)


test by letting x = 5
original:
(8)(3)(6) = 7a + 8(3)
144 = 7a + 24
a = 120/7

in my answer:
a = 5(8)(3)/7 = 120/7
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