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FACTORING POLYNOMIALS (AND DEALING WITH NEGATIVES)

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OBJECTIVE FOR THE DAY

  • Review over factoring quadratics
  • Review over factoring quadratics with numbers
  • Go over how to factor with negatives
  • Go over some examples
  • Go over how to factor negatives with a positive (differing signs)
  • Do some examples
  • Now try some on your own (HW #32)
  • Recap

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Review

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Example 1

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Trial by error

So, let’s try 6*2

2(6) + 2 = 12 + 2 = 14 =/=11

What about 2*6?

2(2) + 6 = 10 =/=11

Not so much, let’s try 3*4

2(3) + 4 = 6 + 4 = 10 =/= 11

So what about:

2(4) + 3 = 8 + 3 = 11 = 11!

So, what we want is (2x + 3)(x + 4)

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So why did we mix our answer?

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And now we solve

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Example 2

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Now we solve

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So, what about when a quadratic has a negative?

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Example 1

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Example 2

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Example 3

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Quadratics with a different sign

So, we’ve seen quadratics with the same signs, but what if they are different signs?

When we see this, we look at our x term.

The reason why is because there will be times that we may have a positive last term, but a negative x term.

This is because 2 negatives multiply to make a positive.

Again, easier to show, so here’s another example:

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Example 4:

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Example 5

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Example 6

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Last Example:

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SO THAT’S PRETTY MUCH IT

That’s pretty much all there is to it to factoring quadratics.

Now the next step is when we can’t factor, but that’s for another time.

As a side note, this is why knowing your divisibility rules is so important.

So, now of course everyone needs to practice.

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Now try some on your own!

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RECAP

  • What you are expected to know from this lesson:
  • How to factor quadratics
  • How to factor quadratics with numbers
  • How to factor quadratics with negatives