Factor t^2+8

Problem

t2+8

Solution

1. Identify the expression as a sum of two terms, t2 and 8

2. Determine if the expression can be factored over the real numbers. Since this is a sum of squares in the form a2+b2 and there is no common factor, it is irreducible over the set of real numbers.

3. Apply the complex factorization pattern a2+b2=(a+b*i)*(a−b*i) if factoring over the complex numbers is required.

4. Rewrite the constant 8 as (√(,8))2 which simplifies to (2√(,2))2

5. Substitute into the complex conjugate pattern to get (t+2*i√(,2))*(t−2*i√(,2))

Final Answer

t2+8=(t+2*i√(,2))*(t−2*i√(,2))

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