Find the exact real root for the equation $10x^3-12x^2-6x-1=0$.
The given cubic cannot be factored easily and beautifully, so the method of factoring the given polynomial is out of the question.
I hear you, the next best approach might be to try out the substitution method, with the hope that after the substitution, we have less variable terms in our newly set equation. But there seems no suitable substitution is available so to make simpler the given equation.
Showing posts with label working backwards. Show all posts
Showing posts with label working backwards. Show all posts
Heuristic Math Problem Solving Skill: Seeing Pattern
Brilliant tudents know how and when to implement heuristic strategies. Heuristic strategies are devices which drastically limits the search for a solution in a large problem space (Polya, 2004).
They provide a general suggestion or technique for solving different types of problems and can be used independently or in combination. The ten most common strategies include:
Working backwards, Finding a pattern, Adopting a different point of view, Solving a simpler analogous problem, Considering extreme cases, Making a drawing, Intelligent guessing and testing, Accounting for all possibilities, Organizing data and logical reasoning (Posamentier, Smith and Stepelman, 2006).
They provide a general suggestion or technique for solving different types of problems and can be used independently or in combination. The ten most common strategies include:
Working backwards, Finding a pattern, Adopting a different point of view, Solving a simpler analogous problem, Considering extreme cases, Making a drawing, Intelligent guessing and testing, Accounting for all possibilities, Organizing data and logical reasoning (Posamentier, Smith and Stepelman, 2006).
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