[Script Info]
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[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.53,0:00:04.02,Default,,0000,0000,0000,,- So we're given a p of x,\Nit's a third degree polynomial,
Dialogue: 0,0:00:04.02,0:00:07.12,Default,,0000,0000,0000,,and they say, plot all the\Nzeroes or the x-intercepts
Dialogue: 0,0:00:07.12,0:00:09.31,Default,,0000,0000,0000,,of the polynomial in\Nthe interactive graph.
Dialogue: 0,0:00:09.31,0:00:10.51,Default,,0000,0000,0000,,And the reason why they\Nsay interactive graph,
Dialogue: 0,0:00:10.51,0:00:13.81,Default,,0000,0000,0000,,this is a screen shot from\Nthe exercise on Kahn Academy,
Dialogue: 0,0:00:13.81,0:00:16.81,Default,,0000,0000,0000,,where you could click\Nand place the zeroes.
Dialogue: 0,0:00:16.81,0:00:20.34,Default,,0000,0000,0000,,But the key here is, lets\Nfigure out what x values make
Dialogue: 0,0:00:20.34,0:00:22.64,Default,,0000,0000,0000,,p of x equal to zero,
Dialogue: 0,0:00:22.64,0:00:23.96,Default,,0000,0000,0000,,those are the zeroes.
Dialogue: 0,0:00:23.96,0:00:25.23,Default,,0000,0000,0000,,And then we can plot them.
Dialogue: 0,0:00:25.23,0:00:26.06,Default,,0000,0000,0000,,So pause this video,
Dialogue: 0,0:00:26.06,0:00:28.38,Default,,0000,0000,0000,,and see if you can figure that out.
Dialogue: 0,0:00:28.38,0:00:32.66,Default,,0000,0000,0000,,So the key here is to try\Nto factor this expression
Dialogue: 0,0:00:32.66,0:00:34.32,Default,,0000,0000,0000,,right over here, this\Nthird degree expression,
Dialogue: 0,0:00:34.32,0:00:36.85,Default,,0000,0000,0000,,because really we're\Ntrying to solve the X's
Dialogue: 0,0:00:36.85,0:00:40.49,Default,,0000,0000,0000,,for which five x to\Nthird plus five x squared
Dialogue: 0,0:00:40.49,0:00:43.07,Default,,0000,0000,0000,,minus 30 x is equal to zero.
Dialogue: 0,0:00:43.07,0:00:44.64,Default,,0000,0000,0000,,And the way we do that is
Dialogue: 0,0:00:44.64,0:00:47.21,Default,,0000,0000,0000,,by factoring this left-hand expression.
Dialogue: 0,0:00:47.21,0:00:48.89,Default,,0000,0000,0000,,So the first thing I always look for
Dialogue: 0,0:00:48.89,0:00:51.14,Default,,0000,0000,0000,,is a common factor\Nacross all of the terms.
Dialogue: 0,0:00:51.14,0:00:55.24,Default,,0000,0000,0000,,It looks like all of the\Nterms are divisible by five x.
Dialogue: 0,0:00:55.24,0:00:57.17,Default,,0000,0000,0000,,So let's factor out a five x.
Dialogue: 0,0:00:57.17,0:00:58.98,Default,,0000,0000,0000,,So this is going to be five x times,
Dialogue: 0,0:00:58.98,0:01:01.37,Default,,0000,0000,0000,,if we take a five x out\Nof five x to the third,
Dialogue: 0,0:01:01.37,0:01:03.04,Default,,0000,0000,0000,,we're left with an x squared.
Dialogue: 0,0:01:03.04,0:01:04.84,Default,,0000,0000,0000,,If we take out a five x\Nout of five x squared,
Dialogue: 0,0:01:04.84,0:01:06.80,Default,,0000,0000,0000,,we're left with an x, so plus x.
Dialogue: 0,0:01:06.80,0:01:09.20,Default,,0000,0000,0000,,And if we take out a\Nfive x of negative 30 x,
Dialogue: 0,0:01:09.20,0:01:13.23,Default,,0000,0000,0000,,we're left with a negative\Nsix is equal to zero.
Dialogue: 0,0:01:13.23,0:01:17.80,Default,,0000,0000,0000,,And now, we have five x\Ntimes this second degree,
Dialogue: 0,0:01:17.80,0:01:20.58,Default,,0000,0000,0000,,the second degree expression\Nand to factor that,
Dialogue: 0,0:01:20.58,0:01:23.23,Default,,0000,0000,0000,,let's see, what two numbers add up to one?
Dialogue: 0,0:01:23.23,0:01:25.11,Default,,0000,0000,0000,,You could use as a one x here.
Dialogue: 0,0:01:25.11,0:01:27.73,Default,,0000,0000,0000,,And their product is\Nequal to negative six.
Dialogue: 0,0:01:27.73,0:01:31.29,Default,,0000,0000,0000,,And let's see, positive\Nthree and negative two
Dialogue: 0,0:01:31.29,0:01:32.55,Default,,0000,0000,0000,,would do the trick.
Dialogue: 0,0:01:32.55,0:01:35.40,Default,,0000,0000,0000,,So I can rewrite this as five x times,
Dialogue: 0,0:01:35.40,0:01:39.51,Default,,0000,0000,0000,,so x plus three, x plus three,
Dialogue: 0,0:01:39.51,0:01:43.41,Default,,0000,0000,0000,,times x minus two, and if\Nwhat I did looks unfamiliar,
Dialogue: 0,0:01:43.41,0:01:46.10,Default,,0000,0000,0000,,I encourage you to review\Nfactoring quadratics
Dialogue: 0,0:01:46.10,0:01:47.32,Default,,0000,0000,0000,,on Kahn Academy,
Dialogue: 0,0:01:47.32,0:01:50.46,Default,,0000,0000,0000,,and that is all going to be equal to zero.
Dialogue: 0,0:01:50.46,0:01:53.17,Default,,0000,0000,0000,,And so if I try to\Nfigure out what x values
Dialogue: 0,0:01:53.17,0:01:54.78,Default,,0000,0000,0000,,are going to make this\Nwhole expression zero,
Dialogue: 0,0:01:54.78,0:01:56.18,Default,,0000,0000,0000,,it could be the x values
Dialogue: 0,0:01:56.18,0:01:58.91,Default,,0000,0000,0000,,or the x value that\Nmakes five x equal zero.
Dialogue: 0,0:01:58.91,0:02:00.21,Default,,0000,0000,0000,,Because if five x zero,
Dialogue: 0,0:02:00.21,0:02:02.98,Default,,0000,0000,0000,,zero times anything else\Nis going to be zero.
Dialogue: 0,0:02:02.98,0:02:06.00,Default,,0000,0000,0000,,So what makes five x equal zero?
Dialogue: 0,0:02:06.00,0:02:09.55,Default,,0000,0000,0000,,Well if we divide five, if\Nyou divide both sides by five,
Dialogue: 0,0:02:09.55,0:02:11.34,Default,,0000,0000,0000,,you're going to get x is equal to zero.
Dialogue: 0,0:02:11.34,0:02:12.45,Default,,0000,0000,0000,,And it is the case.
Dialogue: 0,0:02:12.45,0:02:15.23,Default,,0000,0000,0000,,If x equals zero, this becomes zero,
Dialogue: 0,0:02:15.23,0:02:17.24,Default,,0000,0000,0000,,and then doesn't matter what these are,
Dialogue: 0,0:02:17.24,0:02:18.98,Default,,0000,0000,0000,,zero times anything is zero.
Dialogue: 0,0:02:18.98,0:02:22.05,Default,,0000,0000,0000,,The other possible x value\Nthat would make everything zero
Dialogue: 0,0:02:22.05,0:02:25.46,Default,,0000,0000,0000,,is the x value that makes\Nx plus three equal to zero.
Dialogue: 0,0:02:25.46,0:02:26.92,Default,,0000,0000,0000,,Subtract three from both sides
Dialogue: 0,0:02:26.92,0:02:29.00,Default,,0000,0000,0000,,you get x is equal to negative three.
Dialogue: 0,0:02:29.00,0:02:31.42,Default,,0000,0000,0000,,And then the other x value\Nis the x value that makes
Dialogue: 0,0:02:31.42,0:02:34.05,Default,,0000,0000,0000,,x minus two equal to zero.
Dialogue: 0,0:02:34.05,0:02:37.21,Default,,0000,0000,0000,,Add two to both sides,\Nthat's gonna be x equals two.
Dialogue: 0,0:02:37.21,0:02:38.04,Default,,0000,0000,0000,,So there you have it.
Dialogue: 0,0:02:38.04,0:02:41.15,Default,,0000,0000,0000,,We have identified three x\Nvalues that make our polynomial
Dialogue: 0,0:02:41.15,0:02:43.25,Default,,0000,0000,0000,,equal to zero and those\Nare going to be the zeros
Dialogue: 0,0:02:43.25,0:02:44.77,Default,,0000,0000,0000,,and the x intercepts.
Dialogue: 0,0:02:44.77,0:02:47.83,Default,,0000,0000,0000,,So we have one at x equals zero.
Dialogue: 0,0:02:47.83,0:02:52.26,Default,,0000,0000,0000,,We have one at x equals negative three.
Dialogue: 0,0:02:52.26,0:02:57.26,Default,,0000,0000,0000,,We have one at x equals, at x equals two.
Dialogue: 0,0:02:58.62,0:02:59.83,Default,,0000,0000,0000,,And the reason why it's,
Dialogue: 0,0:02:59.83,0:03:01.37,Default,,0000,0000,0000,,we're done now with this exercise,
Dialogue: 0,0:03:01.37,0:03:02.58,Default,,0000,0000,0000,,if you're doing this on Kahn Academy
Dialogue: 0,0:03:02.58,0:03:04.46,Default,,0000,0000,0000,,or just clicked in these three places,
Dialogue: 0,0:03:04.46,0:03:07.20,Default,,0000,0000,0000,,but the reason why folks\Nfind this to be useful is
Dialogue: 0,0:03:07.20,0:03:10.32,Default,,0000,0000,0000,,it helps us start to think\Nabout what the graph could be.
Dialogue: 0,0:03:10.32,0:03:12.14,Default,,0000,0000,0000,,Because the graph has to intercept
Dialogue: 0,0:03:12.14,0:03:13.90,Default,,0000,0000,0000,,the x axis at these points.
Dialogue: 0,0:03:13.90,0:03:18.36,Default,,0000,0000,0000,,So the graph might look\Nsomething like that,
Dialogue: 0,0:03:18.36,0:03:21.68,Default,,0000,0000,0000,,it might look something like that.
Dialogue: 0,0:03:21.68,0:03:24.02,Default,,0000,0000,0000,,And to figure out what it\Nactually does look like
Dialogue: 0,0:03:24.02,0:03:26.33,Default,,0000,0000,0000,,we'd probably want to try\Nout a few more x values
Dialogue: 0,0:03:26.33,0:03:28.30,Default,,0000,0000,0000,,in between these x intercepts
Dialogue: 0,0:03:28.30,0:03:31.08,Default,,0000,0000,0000,,to get the general sense of the graph.