Question

The polynomials kx³ + 3x² − 8 and 3x³ - 5x + k are divided by x + 2. If the remainder in each case is the same, find the value of k

Answer 1

Given :

• The polynomials kx³ + 3x² − 8 and 3x³ - 5x + k are divided by x + 2. If the remainder in each case is the same

To Find :

• the value of k

Solution :

Let ,

f(x) = kx³ + 3x²- 8

g(x) = 3x³ - 5x + k

Since remainder is same when f(x) and g(x) is divided by x + 2.

f(-2) = g(-2)

k(-2)³ + 3(-2)²- 8 = 3 (-2)³ - 5(-2) + k

k x (-8) + 3 x 4 - 8 = 3 x (-8) + 10 + k

-8k + 12 - 8 = -24 + 10 + k

- 8k + 4 = -14 + k

8k - k = -14 - 4

-9k = -18

k = 2

Answer 2

GivEn :-

• Polynomials kx³ + 3x² − 8 and 3x³ - 5x + k are divided by x + 2 and leaves same reminder.

To FinD :-

• The Value of K in the Polynomial.

CalculaTioN :-

Let,

• f ( x) = kx³ + 3x² − 8

• g (x) = 3x³ - 5x + k

From the Question it clearly states that When f(x) and g(x) are divided by x+2.

• f (-2) = g(-2)

$\sf{k {( - 2)}^{3} + 3 { (- 2)}^{2} - 8 = 3 {( - 2)}^{3} - 5( - 2) + k }{} \\ \\ \sf{k \times ( - 8) + 3 \times 4 - 8 = 3 \times ( - 8) + 10 + k}{} \\ \\ \sf{ - 8k + 12 - 8 = - 24 + 10 + k}{} \\ \\ - 8k + 4 = - 14 + k \\ \\ \sf{ - 8k - k = - 14 - 4}{} \\ \\ \sf{ - 9k = - 18}{} \\ \\ \bf{ \red{k = 2}{} }{}$

Hence value of k = 2