Perform the division and write your answer in form. g(x)+r(x)/ d(x)



(4x^3-1)/ (x-4)

They want you to use polynomial long division. There should be a portion of your reading material or course notes that explains the method. If not, Google the subject for references.

The answer I get is:

4x^2 + 16x + 64 + 255/(x-4)

To perform the division of (4x^3-1) by (x-4), you can use long division. Here's how:

Step 1: Arrange the dividend and divisor in descending order of powers of x:
_______________
x - 4 | 4x^3 + 0x^2 + 0x - 1

Step 2: Divide the first term of the dividend (4x^3) by the first term of the divisor (x):
_______________
x - 4 | 4x^3 + 0x^2 + 0x - 1
- (4x^3 - 16x^2)
_______________
16x^2 + 0x - 1

Step 3: Bring down the next term (-1x^2):
_______________
x - 4 | 4x^3 + 0x^2 + 0x - 1
- (4x^3 - 16x^2)
_______________
16x^2 + 0x - 1
- (16x^2 - 64x)
_______________
64x + 0x - 1

Step 4: Divide the first term of the new polynomial (64x) by the first term of the divisor (x):
_______________
x - 4 | 4x^3 + 0x^2 + 0x - 1
- (4x^3 - 16x^2)
_______________
16x^2 + 0x - 1
- (16x^2 - 64x)
_______________
64x + 0x - 1
- (64x - 256)
_______________
255

Step 5: The division is complete when there are no more terms to bring down or the degree of the remaining polynomial is less than the divisor. In this case, we have a constant term -1 which is less than the divisor, x-4. Therefore, the division is complete.

The final result is:
g(x) = 16x^2 + 64x
r(x) = 255

So, the division of (4x^3-1) by (x-4) can be written as:
(4x^3-1)/(x-4) = 16x^2 + 64x + 255