a. The remainder when the expression x 3 + 9x 2 + bx + c is divided

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a. The remainder when the expression x3 + 9x2 + bx + c is divided by x – 2 is twice the remainder when the expression is divided by x – 1. Show that c = 24.

b. Given that x + 8 is a factor of x3 + 9x2 + bx + 24, show that the equations x3 + 9x2 + bx + 24 = 0 has only one real roots.

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