Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Factor Completely

Factor the polynomial completely.  If the polynomial cannot be factored, say it is prime.

Problem 98; page 58.

x^4 - 1

(x^2 - 1)(x^2 + 1)

The right side factor is prime which means that it cannot be further factored.

The left side factor becomes (x - 1)(x + 1).

Answer:

(x - 1)(x + 1)(x^2 + 1)

Question:

Can I also write the answer this way?

(x - 1)^2(x^2 + 1)

Enjoy your Sunday.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Factor Completely

(x - 1)(x + 1)(x^2 + 1)

Correct!

(x - 1)^2(x^2 + 1)

This is not the same. It is (x-1)(x-1))x^2+1)

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: Factor Completely

(x - 1)(x + 1)(x^2 + 1)

Correct!

(x - 1)^2(x^2 + 1)

This is not the same. It is (x-1)(x-1))x^2+1)

Bob

Thanks.  So, factor completely means showing every factor.