Know the Fundamental Theorem of Algebra and verify it for quadratic polynomials.
Write and verify a quadratic factorization from its roots
Problem
Use the root-to-factor rule \(r↦(x-r)\) for roots \(2\) and \(3\). Multiply the \(\text{two}~\text{factors}\) to verify \(x^{2}-5x+6\).
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What this problem is really about
The root-to-factor rule reverses each root’s sign inside its linear factor. We’ll translate both roots, expand the product, combine the linear terms, and compare every coefficient with the target polynomial to verify the factorization.
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