## Subtitles section Play video

• - [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

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林宜悉 posted on 2020/03/27
Video vocabulary