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Factor k^2 + 8 k + 15

User Daramasala
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To factor a polynomial of the form:


k^2+Bk+C

we need to find two integer numbers, a and b, that fullfil the following:


\begin{gathered} ab=C \\ a+b=B \end{gathered}

then we write the original polynomial as:


k^2+ak+bk+C

finally we factor by agrupation.

Let's do this with the polynomial:


k^2+8k+15

In this case we have that B=8 and C=15. We need two numbers which sum gives 8 and multiplication gives 15; this numbers can be a=5 and b=3, then:


\begin{gathered} 3\cdot5=15 \\ 3+5=8 \end{gathered}

Then we write the polynomial as:


k^2+5k+3k+15

and we factor by agrupation:


\begin{gathered} k^2+8k^2+15=k^2+5k+3k+15 \\ =k(k+5)+3(k+5) \\ =(k+3)(k+5) \end{gathered}

Therefore the factorization of the polynomial is:


(k+3)(k+5)

User Val Berthe
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