Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Extra Factor Completely

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

Problem 122; page 58.

x^4 + x^3 + x + 1

Group A = x^4 + x^3

Group B = x + 1

Factor each group.

Group A

x^4 + x^3

GCF = x^3

x^3(x + 1)

Group B cannot be further factored.

I now have x^3(x + 1) + (x + 1).

(x^3 + 1)(x + 1)(x + 1)

Apply sum of two cubes formula to x^3 + 1.

Doing so, I get this:

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

My final answer is:

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

You say?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Extra Factor Completely

Correct.

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: Extra Factor Completely

Correct.

Bob

Thanks. Believe it or not, I had to speed through these problems because the last 3 or 4 days have been really stressful mentally preparing for my return to work after almost two months unemployed.