1. ## Remainder Theorem

Find the remainder when x^3 + 4x^2 - 7x + 6 is divided by x - 3, by using the remainder theorem, and by long division.

2. P(3) = x^3 + 4x^2 - 7x + 6
P(3) = (3)^3 + 4(3)^2 – 7(3) + 6
P(3) = 27 + 36 – 21 + 6
P(3) = 48

Therefore, the remainder of x^3 + 4x^2 - 7x + 6 divided by x – 3 is 48
This is what I got, is it right? (My first time doing the Remainder Theorem)

3. Originally Posted by Coolman
This is what I got, is it right? (My first time doing the Remainder Theorem)
I believe you're correct - you're working looks fine and checking via long division arrives at the same remainder

4. Originally Posted by e^(i*pi)
I believe you're correct - you're working looks fine and checking via long division arrives at the same remainder
How did you do it via long division? I'm trying and I am not getting the same answer.

5. Originally Posted by Coolman
How did you do it via long division? I'm trying and I am not getting the same answer.
Since my latex sucks when it comes to more than the basics I will scan it in.

Edit 1: the main idea is to divide each term by x initially and then multiply this answer back with the x and the -3. Write that underneath the existing part and then subtract before moving along each power of x until you reach the constant term and that number is the remainder

6. Originally Posted by e^(i*pi)
Since my latex sucks when it comes to more than the basics I will scan it in.

Edit 1: the main idea is to divide each term by x initially and then multiply this answer back with the x and the -3. Write that underneath the existing part and then subtract before moving along each power of x until you reach the constant term and that number is the remainder
Ohhhh, I forgot the three was negative. Thanks!