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Thank you We sneak and here's your smoked you sure

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brought to you by x box That favorite gaming system

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of mathematicians followed closely by x squared box Which of

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the following is a factor of x cubed minus six

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x squared plus five x plus twelve And here the

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potential answer All right so we just tried asking each

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of the answer choices if they were a factor of

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the polynomial But well none of them answered Totally unhelpful

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Thanks guys Tactic number two we figure it out ourselves

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We know that if an expression is the factor of

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a polynomial any roots of the expression must be routes

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of the polynomial And a root of an expression is

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where the expression is equal to zero So if we

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want to test whether an expression is a factor of

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a polynomial we'll have to set it equal to zero

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and then solve for x Well after that we can

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substitute the value we get into the equation And if

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the whole thing ends up peopling zero then the expression

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is a factor or route of the polynomial down confusing

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and let's Just see it in action Going with option

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a x minus two if we set that equal to

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zero i e x minus two equals zero We would

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add to to both sides and get x equals two

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Now we just take our x value and substitute it

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into the original equation We get two cubed minus six

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times two Squared plus five times two plus twelve which

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simplifies to eight minus twenty four plus ten plus well

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and that whole jumbled mess comes out tio six Well

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whether or not it's a master of disguises six is

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no zero so is out We'll try the same thing

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with option b x plus one here will set that

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equal to zero then subtract one from both sides to

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get x equals negative one and we plug in negative

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one for ex well naked one cubed minus six times

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negative one squared plus five times negative one plus twelve

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as we get that all simplifies too negative one minus

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six minus five plus twelve which comes out to wait

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for it Zero that's the face of a winner We

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could do the same for option cnd but since we

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already found the one factor that works there's not really

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any need go further unless we're really starved for entertainment 00:02:15.53 --> [endTime] and maybe invest in an xbox

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