Question

a= -3, remainder = -4
Answer​

Answer 1

ANSWER:---------

according to the question, when the polynomial p(x) = 2x^3 - 3x^2 + ax - 3a + 9 is divided (x + 1), remainder is 16.

x = -1 (since x + 1 =  0)

⇒ p(-1) = 2(-1)^3 - 3(-1)^2 + a(-1) - 3a + 9 = 16

⇒ -2 - 3 - a - 3a + 9 = 16

⇒ -5 - 4a + 9 = 16

⇒ 4 - 4a = 16

⇒ -4a = 16 - 4

⇒ -4a = 12

⇒ 4a = -12

⇒ a = -12/4

⇒ a = -3

now, when p(x) is divided by (x + 2)

p(-2) = 2(-2)^3 - 3(-2)^2 + (-3)(-2) - 3(-3) + 9

= -16 - 12 + 6 + 9 + 9

= -28 + 24

= -4

hence, the remainder is -4.

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