Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Long Division

Divide 1 - x^2 + x^4 by x^2 + x + 1.

I rewrote the dividend this way:

x^4 + 0x^3 - x^2 + 0x + 1

For those who have the book, this is problem 101 on page 49.

I got x^2 - x - 1 with remainder 2.

My quotient is correct. According to the book the remainder is 2x + 2.

I think this is a typo. You say?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Long Division

I get that remainder. What did you get for the quotient?

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Long Division

I get that remainder. What did you get for the quotient?

Bob

My quotient is x^2 - x - 1 with remainder 2.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Long Division

That quotient is correct.  The last subtract should be:

- x^2 + x + 1
-x^2    -x  - 1

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Long Division

That quotient is correct.  The last subtract should be:

- x^2 + x + 1
-x^2    -x  - 1

Bob

Your last subtract set up leads yo the correct remainder:

2x + 2.

I guess the book is right.