Question

If the polynomial ax3 + 4x2 + 3x - 4 and x3 - 47 + a leave the same remainder when divided by x-3 find the value of a

Answer 1

Answer:

a = - 61 / 26

Step-by-step explanation:

Let's write

f(x) = a x³ + 4 x² + 3 x - 4

and

g(x) = x³ - 47 + a.

The remainder when divided by x-3 is simply the value at 3.  [ To see this, if we divide f(x) by x-3, we end up with f(x) = (x-3) × something + remainder, so f(3) = remainder. ]

So the remainder when f(x) is divided by x-3 is

f(3) = 27 a + 36 + 9 - 4 = 27 a + 41

and the remainder when g(x) is divided by x-3 is

g(3) = 27 - 47 + a = a - 20.

Since the remainders are the same, we get the equation for a :

27 a + 41 = a - 20

=> 26 a = - 61

=> a = - 61 / 26