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042b538e-c3e9-4e3d-a782-3ed7c630fa14.html
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<p>To help students consolidate the observations and insights from this lesson, consider asking them to describe to a partner or write down their responses to prompts such as:</p>
<ul>
<li> "How would you explain to a classmate who is absent today how to rewrite \(x^2+ 16x − 36\) in factored form?" (Check to make sure the leading coefficient on the \(x^2\) term is 1. Then look for factors of the constant term, –36, that result in a sum of the linear term, +16. We know that one factor must be positive and one factor must be negative. Use these factors to convert the expression into the factored form, \((x + m)(x + n)\). Since the factors we are looking for are 18 and –2, the factored form is \((x + 18)(x − 2)\). </li>
<li>"How would you explain how to rewrite \(x^2−5x −24\) in factored form?" (Check to make sure the leading coefficient on the \(x^2\) term is 1. Then look for factors of the constant term, –24, that result in a sum of the linear term, –5. We know that one factor must be positive and one factor must be negative. Use these factors to convert the expression into the factored form, \((x + m)(x + n)\). Since the factors we are looking for are –8 and 3, the factored form is \((x − 8)(x + 3)\). </li>
<li>"Suppose you are rewriting the quadratic expression \(x^2+bx +c\) in factored form \((x + m)(x + n)\). How will the factors be different when the \(c\) is positive versus when \(c\) is negative?" (When \(c\) is positive, we know that the factors of \(c\) we are looking for have the same sign. When \(c\) is negative, we know that the factors of \(c\) we are looking for have opposite signs.) </li>
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