Question

if the polynomial P(x)= 2x^3 - 3x^2 + 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
STEP BY STEP PLEASE​

Answer 1

Answer:

Step-by-step explanation:

Hello Dear.

Here is the answer---

Given Polynomial ⇒

P(x) = x⁴ - 2x³ + 3x² - ax + 3a - 7.

Divisor = x + 1

∴ x + 1 = 0

∴ x = -1

Thus,

P(-1) = (-1)⁴ - 2(-1)³ + 3(-1)² - a(-1) + 3a - 7.

19 = 1 + 2 + 3 + a + 3a - 7

19 = 6 - 7 + 4a

4a - 1 = 19

4a = 20

⇒ a = 4

∴ Value of a is 4.

Now, the Polynomial will be ---→

P(x) = x⁴ - 2x³ + 3x² - (4)x + 3(4) - 7

P(x) = x⁴ - 2x³ + 3x² - 4x + 12 - 7

P(x) = x⁴ - 2x³ + 3x² - 4x + 5

Now, When this polynomial is divided by (x + 2), then,

x + 2 = 0

x = - 2

∴ P(-2) = (-2)⁴ - 2(-2)³ + 3(-2)² - 4(-2) + 5

⇒ P(-2) = 16 + 16  + 12 + 8 + 5

⇒ P(-2) = 57

Thus, Remainder will be 57.

Hope it helps.

Answer 2

Hey dude,

Given Polynomial ⇒

P(x) = x⁴ - 2x³ + 3x² - ax + 3a - 7.

Divisor = x + 1

∴ x + 1 = 0

∴ x = -1

Thus,

P(-1) = (-1)⁴ - 2(-1)³ + 3(-1)² - a(-1) + 3a - 7.

19 = 1 + 2 + 3 + a + 3a - 7

19 = 6 - 7 + 4a

4a - 1 = 19

4a = 20

⇒ a = 4

∴ Value of a is 4.

Now, the Polynomial will be ---→

P(x) = x⁴ - 2x³ + 3x² - (4)x + 3(4) - 7

P(x) = x⁴ - 2x³ + 3x² - 4x + 12 - 7

P(x) = x⁴ - 2x³ + 3x² - 4x + 5

Now, When this polynomial is divided by (x + 2), then,

x + 2 = 0

x = - 2

∴ P(-2) = (-2)⁴ - 2(-2)³ + 3(-2)² - 4(-2) + 5

⇒ P(-2) = 16 + 16  + 12 + 8 + 5

⇒ P(-2) = 57

Thus, Remainder will be 57.

@DevanKey02