Algebraic Pattern Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

medium
Simplify x3+8x+2\frac{x^3 + 8}{x + 2}.

Solution

  1. 1
    x3+8=(x+2)(x2โˆ’2x+4)x^3 + 8 = (x+2)(x^2 - 2x + 4) (sum of cubes).
  2. 2
    (x+2)(x2โˆ’2x+4)x+2=x2โˆ’2x+4\frac{(x+2)(x^2-2x+4)}{x+2} = x^2 - 2x + 4, xโ‰ โˆ’2x \neq -2.

Answer

x2โˆ’2x+4x^2 - 2x + 4, xโ‰ โˆ’2x \neq -2
Recognizing the numerator as a sum of cubes enables factoring and cancellation. Without pattern recognition, this simplification would require polynomial long division.

About Algebraic Pattern

A recognizable, recurring algebraic structure such as a2โˆ’b2a^2 - b^2 or (a+b)2(a+b)^2 that can be applied systematically.

Learn more about Algebraic Pattern โ†’

More Algebraic Pattern Examples

Example 1 easy

Identify the pattern and factor: [formula].

Example 2 hard

Factor [formula] by identifying the pattern.

Example 3 easy

What pattern does [formula] match?

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