Question

The polynomial ax

3 + 4x2 + 3x – 4 and x

3

– 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:

According to remainder theorem, if f(x) is divided by (x-a)then remainderis f(a)

f(x) = ax³+4x²+3x-4

g(x)= x³-4x +a

f(3)=A(27)+4(9)+3(3)-4

27a+41

g(3)=27-4(3)+a

15+a

f(3)=G(3)

27a+41=15+a

26a=15-41

a=15-41/26

a=-26/26

a=-1

Answer 2

Given:

ax³ + 4x² +3x - 4 and x³ - 4x + a

To Find:

the value of a.

Solution:

f(x) = ax³ + 4x² + 3x - 4

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

f(3) = 27a + 41

Now,

g(x) = x³ - 4x + a

g(3) = 27 - 4(3) + a

g(3) = 15 + a

Then,

f(3) = g(3)

27a + 41 = 15 + a

26a = 15 - 41

26a = -26

a = -26/26

a = -1

Therefore, the value of a = -1.