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When the polynomial mx^3-3x^2+nx+2 is divided by x+3, the reminder is -1. When it is divided by x-2, the reminder is -4. What are the values of m and n?

Respuesta :

nobillionaireNobley
Let f(x) = mx^3 - 3x^2 + nx + 2
(mx^3 - 3x^2 + nx + 2) ÷ (x + 3) has a remainder of -1 implies that f(-3) = -1
m(-3)^3 - 3(-3)^2 + n(-3) + 2 = -1
-27m - 27 - 3n + 2 = -1
27m + 3n = -24
9m + n = -8 . . . (1)

(mx^3 - 3x^2 + nx + 2) ÷ (x - 2) has a remainder of -4 implies that f(2) = -4
m(2)^3 - 3(2)^2 + n(2) + 2 = -1
8m - 12 + 2n + 2 = -1
8m + 2n = 9 . . . (2)

(1) * 2 => 18m + 2n = -16 . . . (3)
(2) - (3) => -10m = 25
m = 25/-10 = -5/2

From (2), 9(-5/2) + n = -8
n = -8 + 45/2 = 29/2

Therefore, m = -5/2, n = 29/2

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