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 116; page 58.

(5x + 1)^3 - 1

Difference of two cubes formula:

(x - a)(x^2 + ax + a^2)

Let x = 5x and a = 1.

Note: 1 can be written as 1^3.

Apply formula.

(5x - 1)((5x)^2 + 5x + 1)

(5x - 1)(25x^2 + 5x + 1)

You say?

Last edited by mathxyz (2024-05-20 14:37:01)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Extra Factor Completely

Right idea but it went wrong here:

Let x = 5x and a = 1.

That should be "x" = 5x +1.  I've put "x" because that x is the one in the cube formula and it's different from the x in the question.

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: Extra Factor Completely

Right idea but it went wrong here:

Let x = 5x and a = 1.

That should be "x" = 5x +1.  I've put "x" because that x is the one in the cube formula and it's different from the x in the question.

Bob

Thanks. Let me see.

Let x = 5x + 1

Let a = 1.

Difference of cubes formula:

(x - a)(x^2 + ax + a^2)

(5x + 1 - 1)((5x + 1)^2 +1(5x + 1) + 1^2)

(5x)(25x^2 + 10x + 1 + 5x + 1 + 1)

(5x)(25x^2 + 15x + 3)

It looks a little weird.

Is that it?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Extra Factor Completely

That is indeed it. Problem done!

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: Extra Factor Completely

That is indeed it. Problem done!

Bob

Very cool.