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June 5th, 2014, 11:39 PM   #1
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Factoring Polynomials

Hi all,

I've just watched a video on youtube

Algebra 2 - Dividing Polynomials - YouTube

where x^2+6x+5 / x+1 was factored. His result was

(x+5)(x+1) / (x+1)

Why didn't he factor / consider the 6x ? I admit that I havent started to learn how to factor polynomials and my question is purely out of curiosity.

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Mike
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June 5th, 2014, 11:53 PM   #2
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For $x^2 +bx +c$ there are two roots $x = r_1$ and $x = r_2$ so that the equation is
$$(x - r_1)(x - r_2)$$
If we multiply out the brackets we get
$$x^2 - (r_1 + r_2)x + r_1 r_2$$

So $c$ is the product of the two roots and $b$ is minus the sum of the two roots.

In the case of your example, the only pair of integers that multiply to make 5 are 1 and 5, so those are the roots to try.

Any quadratic $x^2 + bx + c$ where $b$ and $c$ are both integers can have two integer roots or two irrational roots or no real roots at all.
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Last edited by v8archie; June 5th, 2014 at 11:56 PM.
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June 6th, 2014, 01:01 AM   #3
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Thanks for that its always helpful to know why!
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Mike
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