Question

The polynomials kx3+3x2-3 and 2x3-5x+k when divided by x-4 leave the same remainder in each case. Then find the value of k

Answer 1

Answer:K=1

Step-by-step explanation:

Put X=4 in both equation

And both eq would be equal to each other

Answer 2

The value of k is 1.

Step-by-step explanation:

Given: Two polynomials $kx^3+3x^2-3$ and $2x^3-5x+k$

When divided by x-4, leave the same remainder

To find: Value of k

Concept Used: After substituting x = 4, the expressions obtained for both equations would be the same.

Solution:

• Substituting x = 4 in Equation (1)

$kx^3+3x^2-3$

$k(4)^3+3(4)^2-3$

$64k+48-3$

$64k+45$

• Similarly, substituting x = 4 in Equation (2)

$2x^3-5x+k$

$2(4)^3-5(4)+k$

$128-20+k$

$108 + k$

• Equating the results

$64k+45=108 + k$

$64k-k=108- 45$

$63 k =63$

$k=1$

• Hence, the value of k is 1.