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  • - [Instructor] So let's see if we can try to factor

  • the following expression completely.

  • So factor this completely,

  • pause the video and have a go at that.

  • All right, now let's work through this together.

  • So the way that I like to think about it,

  • I first try to see is there any common factor

  • to all the terms, and I try to find the greatest

  • of the common factor,

  • possible common factors to all of the terms.

  • So let's see, they're all divisible by two,

  • so two would be a common factor,

  • but let's see, they're also all divisible by four,

  • four is divisible by four, eight is divisible by four,

  • 12 is divisible by four,

  • and that looks like the greatest common factor.

  • They're not all divisible by x,

  • so I can't throw an x in there.

  • So what I wanna do is factor out a four.

  • So I could re-write this as four times,

  • now what would it be, four times what?

  • Well if I factor a four out of four x squared,

  • I'm just going to be left with an x squared.

  • If I factor a four out of negative eight x,

  • negative eight x divided by four is negative two,

  • so I'm going to have negative two x.

  • And if I factor a four out of negative 12,

  • negative 12 divided by four is negative three.

  • Now am I done factoring?

  • Well it looks like I could factor this thing

  • a little bit more.

  • Can I think of two numbers that add up to negative two,

  • and when I multiply it I get negative three,

  • since when I multiply I get a negative value,

  • one of the 'em is going to be positive

  • and one of 'em is going to be negative.

  • I can think about it this way.

  • A plus B is equal to negative two,

  • A times B needs to be equal to negative three.

  • So let's see, A could be equal to negative three

  • and B could be equal to one

  • because negative three plus one is negative two,

  • and negative three times one is negative three.

  • So I could re-write all of this

  • as four times x plus negative three,

  • or I could just write that as x minus three,

  • times x plus one, x plus one.

  • And now I have actually factored this completely.

  • Let's do another example.

  • So let's say that we had the expression

  • negative three x squared plus 21 x minus 30.

  • Pause the video and see if you can factor this completely.

  • All right now let's do this together.

  • So what would be the greatest common factor?

  • So let's see, they're all divisible by three,

  • so you could factor out a three.

  • Let's see what happens if you factor out a three.

  • This is the same thing as three times,

  • well negative three x squared divided

  • by three is negative x squared,

  • 21 x divided by three is seven x, so plus seven x,

  • and then negative 30 divided by three is negative 10.

  • You could do it this way,

  • but having this negative out on the x squared term

  • still makes it a little bit confusing

  • on how you would factor this further.

  • You can do it, but it still takes

  • a little bit more of a mental load.

  • So instead of just factoring out a three,

  • let's factor out a negative three.

  • So we could write it this way.

  • If we factor out a negative three, what does that become?

  • Well then if you factor out a negative three out

  • of this term, you're just left with an x squared.

  • If you factor out a negative three from this term,

  • 21 divided by negative three is negative seven x.

  • And if you factor out a negative three out of negative 30,

  • you're left with a positive 10, positive 10.

  • And now let's see if we can factor this thing

  • a little bit more.

  • Can I think of two numbers where if I were to add them

  • I get to negative seven,

  • and if I were to multiply them, I get to 10?

  • And let's see, they'd have to have the same sign

  • 'cause their product is positive.

  • So let's see A could be equal to negative five,

  • and then B is equal to negative two.

  • So I can re-write this whole thing as equal

  • to negative three times x plus negative five,

  • which is the same thing as x minus five,

  • times x plus negative two,

  • which is the same thing as x minus two.

  • And now we have factored completely.

- [Instructor] So let's see if we can try to factor

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A2 negative factor divisible squared divided equal

Worked examples factoring completely

  • 18 0
    林宜悉 posted on 2020/03/27
Video vocabulary