Question

If the polynomial p (x) = 2x - 3x2 + ax - 3a +9 is divided
by x + 1, the remainder is 16. Find the value of a. Also
find the remainder when p(x) is divided by x + 2.
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Answer 1

Answer:

Step-by-step explanation:

Answer 2

GiveN Polynomial:

p(x)= 2x³- 3x² + ax - 3a + 9

Remainder is 16 when divided by x + 1

And then divided by x + 2

To FinD:

Value of a?

Remainder when divided by x + 2

Step-by-Step Explanation:

When we divide p(x) by x + 1, the remainder will be p(-1)

So,

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

⇒ p(-1) = 2(-1) - 3(1) - a - 3a + 9

⇒ p(-1) = -2 - 3 - 4a + 9

⇒ p(-1) = 4 - 4a

According to question,

⇒ p(-1) = 16

⇒ 4 - 4a = 16

⇒ -4a = 12

⇒ a = -3

Thus, the required value of a is -3 (Ans)

So, Our polynomial will be now:

⇒ p(x) = 2x³- 3x² + (-3)x - 3(-3) + 9

⇒ p(x) = 2x³ - 3x² - 3x + 18

When we divide p(x) by x + 2, the remainder will be p(-2)

⇒ p(-2) = 2(-2)³ - 3(-2)² - 3(-2) + 18

⇒ p(-2) = 2(-8) - 3(4) + 6 + 18

⇒ p(-2) = -16 - 12 + 24

⇒ p(-2) = -28 + 24

⇒ p(-2) = -4

Thus, the required remainder is -4 (Ans)