Factor quadratics to reveal zeros of the function they define.
Write a quadratic from zeros and scale factor
Problem
Write a quadratic with zeros \(2\) and \(5\) and scale factor \(1\). Convert each zero to a linear factor, assemble the factored function, and substitute both zeros to check it.
Big Picture
What this problem is really about
A zero r becomes the factor x minus r, while the scale factor multiplies the entire factor product. We’ll convert each supplied zero with the correct sign, apply the scale, expand to standard form, and substitute both roots to verify the zeros and leading coefficient.
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