Use expression structure to identify useful rewrites, such as difference-of-squares factoring.
Rewrite a quadratic to reveal its zeros
Problem
Rewrite \(f(x)=x^{2}-5x+6\) in factored form to reveal every zero. Use product-and-sum evidence, state each multiplicity, verify by substitution, and compare the intercepts with the displayed answer graph.
Big Picture
What this problem is really about
Factored form exposes zeros only after the factorization has been justified. We’ll find the integer pair that matches both the constant product and signed linear sum, expand to verify equivalence, then solve every factor, record multiplicities, and check the resulting inputs in the original function.
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