The polynomials x cube 3 x square - 3 and 2 x cube minus 5x a leave the same remainder in each case when divided by x minus 4 find the value of.


To find the value of x, we need to use the remainder theorem. The remainder theorem states that if a polynomial P(x) is divided by x - a, then the remainder is P(a).


We need to find the remainder when x cube + 3x square - 3 is divided by x - 4. To do this, we can use long division or synthetic division.




Therefore, the remainder is 109 when x cube + 3x square - 3 is divided by x - 4.




Therefore, the remainder is 25 when x cube + 3x square - 3 is divided by x - 4.


We need to find the value of k such that 2x³ - 5x + k leaves the same remainder as x cube + 3x square - 3 when divided by x - 4.

Let R(x) be the remainder when 2x³ - 5x + k is divided by x - 4. By the remainder theorem, we know that R(4) = 109.



Therefore, when 2x³ - 5x + 123 is divided by x - 4, the remainder is 123.


We need to find the value of k.

Since the remainder is the same in both cases, we have:

R(x) = 2x³ - 5x + k - (x cube + 3x square - 3) = 2x³ - x² - 5x + (k + 3)

We know that R(4) = 109, so we have:

2(4)³ - 4² - 5(4) + (k + 3) = 109

Simplifying this equation, we get:

k = -150

Therefore, the value of k is -150.