What is the best strategy for finding coefficients, given the following scenarios:

A. Distinct linear factors. Ex: \(\displaystyle (x + 3) (x + 2)\) etc..

Equation System, or Substitution method

B. Repeated Linear Factors Ex \(\displaystyle (x + 3)^{2}\) or \(\displaystyle x^{2}\)

?

C. Irreducible Quadratic \(\displaystyle (x^{2} + 25)\)

Equation System only ??

Can we use an equation system in all cases? I think not, as was not the case in one problem.

A. Distinct linear factors. Ex: \(\displaystyle (x + 3) (x + 2)\) etc..

Equation System, or Substitution method

B. Repeated Linear Factors Ex \(\displaystyle (x + 3)^{2}\) or \(\displaystyle x^{2}\)

?

C. Irreducible Quadratic \(\displaystyle (x^{2} + 25)\)

Equation System only ??

Can we use an equation system in all cases? I think not, as was not the case in one problem.

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