What is the factored form of x 3 1

Q: How do you find the factored form?

When the given equation can be expressed in the form a2 - b2, it can be factored as (a+b)(a−b) ( a + b ) ( a − b ) . Example: Consider y2−100 y 2 − 100 . Each of the terms here can be expressed in the form of square. Here the factors are (y+10 ) and (y−10) .

We think you wrote:

Table of Contents Show

Step by Step Solution
Step 1 :
Final result :
Why learn this
Terms and topics
Related links
How do you find the factored form?
What is the factor of x³ Y³?
What's a factored form?

This solution deals with simplification or other simple results.

Step by Step Solution

Step 1 :

Trying to factor as a Difference of Cubes:

1.1 Factoring: x3-1

Theory : A difference of two perfect cubes, a3 - b3 can be factored into
(a-b) • (a2 +ab +b2)

Proof :  (a-b)•(a2+ab+b2) =
            a3+a2b+ab2-ba2-b2a-b3 =
            a3+(a2b-ba2)+(ab2-b2a)-b3 =
            a3+0+0-b3 =
            a3-b3

Check : 1 is the cube of 1
Check : x3 is the cube of x1

Factorization is :
(x - 1) • (x2 + x + 1)

Trying to factor by splitting the middle term

1.2 Factoring x2 + x + 1

The first term is, x2 its coefficient is 1 .
The middle term is, +x its coefficient is 1 .
The last term, "the constant", is +1

Step-1 : Multiply the coefficient of the first term by the constant 1 • 1 = 1

Step-2 : Find two factors of 1 whose sum equals the coefficient of the middle term, which is 1 .

	-1	+	-1	=	-2
	1	+	1	=	2

Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored

Final result :

  (x - 1) • (x2 + x + 1)

Why learn this

Terms and topics

#x^3 -1 = (x-1)(x^2 +x +1)#

Explanation:

This is a type of factorising called the the sum or difference of two cubes:

#a^3 - b^3 = (a-b)(a^2+ab +b^2)#

The sum of cubes is factored as:

#a^3 + b^3 = (a+b)(a^2-ab +b^2)#

In this case we have: #x^3 -1# so follow the rule above.

#x^3 -1 = (x-1)(x^2 +x +1)#

How do you find the factored form?

When the given equation can be expressed in the form a² - b², it can be factored as (a+b)(a−b) ( a + b ) ( a − b ) . Example: Consider y2−100 y 2 − 100 . Each of the terms here can be expressed in the form of square. Here the factors are (y+10 ) and (y−10) .

What is the factor of x³ Y³?

The sum of cubes, x³ + y³, can be factored as x³ + y³ = (x + y)(x² – xy + y²).

What's a factored form?

factored form (of a quadratic expression) A quadratic expression that is written as the product of a constant times two linear factors is said to be in factored form.