Question

12. If the polynomials axcube+ 4x² + 3x - 4 and xcube - 4x + a leave the same remainder when
divided by x-3,find the value of a​

Answer 1

Answer:

a = -1

Step-by-step explanation:

Given:-

f(x)= ax³ + 4x² + 3x - 4

&

P(x) = x³ - 4x + a

Both of their Remainder comes same when divided by x-3

Refer attachment for division process

Now we get ,

$R_1$ = {3 +3(3a +4)}x - 4 .......(i)

as remainder of f(x).

$R_2$ = 5x + a .....(ii)

as remainder of P(x).

Now equate both the equations as both are same [°•° R1 = R2 ]

Solve as follows:-

{3 +3(3a +4)}x - 4 = 5x + a

{ 9a + 15}x - 4 = 5x + a

9ax + 15x - 4 = 5x + a

9 ax + 10x = a + 4

As (x-3) is the factor of polynomial so x= 3 is its solution

Now put x = 3

9 a(3) + 10(3)= a + 4

27a + 30 = a +4

26a = -26

a = -1

a = -1

Answer 2

hey there

refer to attachment