algebra 2 question

Question

  could someone explain what the remainder would be for this

f (x)=3x^6+82^3+27

Answer 1

Using the Remainder Theorem

Step1:

Remainder Theorem states that when a polynomial f(x) is divided by (x - a), the remainder is simply f(a).

Representation:

Remainder = f(a)

Step 2:

If you are given the following divisions:

(x – 2), then a = 2

(x – 3), then a = -3

Step 3:

Your main function is: f(x) = 3x⁶ + 82³ + 27      Note: 82³ = 551,368

f(x) = 3x⁶ + 551,368 + 27 = 3x⁶ + 551,395

Step 4: 

Compute f(a)

Substitute chosen a into f(x): f(a) = 3a⁶ + 551,395

The answer is the remainder when dividing f(x) by (x - a)

For Instance,

If divisor = (x - 2)

f(2) = 3(2)⁶ + 551,395 = 3(64) + 551, 395 = 551,587

If divisor = (x + 3):

f(-3) = 3(-3)⁶ + 551,395 = 3(729) + 551, 395 = 2,187 + 551, 395 = 553,582