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All right sy mash bumpers Another question for you Here

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we go Which of the following are the solutions to

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the equation Negative ninety squared plus fifteen year plus six

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Zero hello quadratic ce All right well let's grab historical

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and dive right into solving This is puffy here while

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exploring the depths of the ocean We don't recommend sticking

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heads or hands in tow dark holes where squid like

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creatures could be lurking Avoid tangling with the easy ones

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in particular Alright so pulling out a g c f

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of negative three from each term shines a light on

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how to proceed and you'll scare a few fish by

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doing that so let's do this thing negative three pulled

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out gets us was that three z squared minus five

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z minus two zero Well the negative three casts an

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ominous shadow on the tri no menial three z squared

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minus five c minus to scare it away by dividing

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the entire equation by negative three including that zero on

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the far right If only sharks were afraid of division

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to all right so that's what it gives us right

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here rewrite the middle term of trento meal by identifying

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factors of well it's a negative to there and times

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three which is negative six on the end got to

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find them also to be ableto add two negative five

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so well let's see negative six and one work because

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well negative six times one is negative six and the

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negative six plus ones Negative five So negative five z

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can be re written as yes negative six z plus

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z and notice Pulling out the z's in the middle

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of nowhere like this and problems seems to be the

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key for a whole lot of these questions If you

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could do it fluidly well you'll score a whole bunch

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of points on this exam Okay so moving on group

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the first two terms the last two terms and apology

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cf out of each group So we'll group him like

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this three z squared minus sixty plus z minus two

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And we can pull three z out of this thing

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here while realizing z minus two is a factor of

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both terms Like finding a beautiful pearl inside of a

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clam factor that by no meal out and that gets

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us well z minus two quantity three z plus one

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zero and for the entire equation equals zero Either one

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or both of the factors must equals zero right So

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we saw for zeon Both of them start just by

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setting z minus two Equal to zero and miles equals

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two Beautiful Do the same thing with second factor three

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z plus one and well three z then is negative

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one so we divide three on both sides so z

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then is negative a third with the grace of a

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mermaid or a large man Iti we recover the solutions

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off Negative ninety square plus fifteen z plus six equals

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zero which are z equals two and c equals negative

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A third it's just that's it We're done We're shmoop 00:02:33.863 --> [endTime] what

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