Factor x^3+1

Problem

x3+1

Solution

1. Identify the expression as a sum of two cubes, which follows the general form a3+b3

2. Determine the values of a and b by taking the cube roots of each term.

a=√(3,x3)=x

b=√(3,1)=1

3. Apply the formula for the sum of cubes, which is a3+b3=(a+b)*(a2−a*b+b2)

4. Substitute the values of a and b into the formula.

(x+1)*(x2−(x)*(1)+1)

5. Simplify the terms inside the second set of parentheses.

(x+1)*(x2−x+1)

Final Answer

x3+1=(x+1)*(x2−x+1)

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