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This is a practice assignment. This factoring quadratics, algebra 1.

This is a practice assignment. This factoring quadratics, algebra 1.-example-1
User Jake McGraw
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1 Answer

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To factor a quadratic polynomial of the form:


n^2+bn+c

we need to find to intergers B and C that fulfill the following conditions:


\begin{gathered} BC=c \\ \text{and} \\ B+C=b \end{gathered}

In the case of the polynomial:


n^2-4n-32

we notice that b=-4 and c=-32. Then we need to find two numbers that fulfills:


\begin{gathered} -32=BC \\ -4=B+C \end{gathered}

if we choose B=-8 and C=4 we notice that this requierements are fulfill. Once we have this numbers we write the polynomial as:


n^2-8n+4n-32

and we factor the first two terms and the last two terms by common factors:


\begin{gathered} n^2-4n-32=n^2-8n+4n-32=n(n-8)+4(n-8) \\ =(n-8)(n+4) \end{gathered}

Therefore:


n^2-4n-32=(n-8)(n+4)

User Dimmg
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