Math CentralQuandaries & Queries


Question from Eric, a student:

2v(squared) +11v +5

Hi Eric,

You didn't give any instructions but I think you are to factor this expression. Thus you want to find integers $a, b, c$ and $d$ so that

\[2v^2+11v+5= (av + b)(cv + d).\]

If you expand the right side the $v^2$ term is $acv^{2}.$ But this has to be $2v^2$ if the two sides are equal. Since $a$ and $c$ are integers either one is 2 and the other is 1 or one is -2 and the other is -1. Let's stick with the positive ones and, since the order of multiplication doesn't let's say that $a = 2$ and $c = 1.$ thus you have

\[2v^2+11v+5= (2v + b)(v + d).\]

If you expand the right side what is the constant term? What does this tell you about $b$ and $d?$ You have some choices. Which one gives the term $11v$ when you expand the right side?

Write back if you need more help,

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