Need Help Factoring x^3 + 8? Quick and Easy Solutions Available!

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To factor the expression x^3 + 8, recognize it as a sum of cubes, which can be expressed as (x + 2)(x^2 - 2x + 4). The formula used is a^3 + b^3 = (a + b)(a^2 - ab + b^2), with a = x and b = 2. To find factors, apply the Remainder and Factor Theorems by testing values like f(1), f(-1), and f(2) to identify roots. In this case, f(-2) = 0 indicates that x + 2 is a factor, and synthetic or long division can be used to determine the remaining factor.
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Can someone help me factor x^3 + 8? I totally forgot how to do that :S
 
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We must note that this is an expression of the form a^3+b^3=(a+b)(a^2-ab+b^2), where in this case a=x and b=2.
 
Usually to factor things ,use the remainder and Factor theorem.

Let f(x)=x^3 + 8
try f(1,-1,2,etc) and when you get x=a such that f(a)=0. x-a is a factor of f(x)

For your example; f(-2)=0 so that x+2 is factor of f(x)...you can use synthetic division or long division to get the other factor.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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