Last class, we saw that we could factor trinomials that had no leading coefficient (they look like

.  Often, trinomials may have a leading coefficient and look like: .

When you are presented with any factoring problem, you should always look for the greatest common factor (GCF) first.  Sometimes, it will change your trinomial to something that could be more easily factored.  Other times, you will be left with a leading coefficient, and another method of factoring needs to be considered.

Things you should know after today:

  • Always look for a GCF first when factoring
  • Factoring trinomials by decomposition
  • Determine when a trinomial can be factored

Resources

  • Notes

Assignment

  • Worksheets
  • 5.3 Extra Practice from your notes booklet
  • p234 #2, 3, 6, 7, 8b, 11, 12, 15, 18, 19
Attachments:
FileDescriptionFile size
Download this file (10.5.3b.decomposition.notes.pdf)10.5.3b.decomposition.notes.pdf 143 kB
Download this file (10.5.3b.notes.pdf)10.5.3b.notes.pdf 3836 kB

A second kind of factoring involves taking trinomials in the format:

.  These have no leading coefficient in front of the term and can basically be factored using the opposite of the shortcut that you developed in 5.1

Things you should be able to do after today:

  • factor trinomials of the type 
  • determine when a trinomial might not be factorable
  • determine possible factors when the middle term might be unknown.

Resources

  • Notes

Assignment

  • p234 #1, 4, 5, 8a, 9, 10, 13, 16
  • Worksheets
  • Extra Practice 5.3
Attachments:
FileDescriptionFile size
Download this file (10.5.3.notes.pdf)10.5.3.notes.pdf 3427 kB

Multiplying out polynomial factors and collecting like terms is sometimes called "expanding" and "simplifying".  However, it is also possible to take a polynomial and change it back into the multiplication question that you started from. This process is called "factoring".  There are many different ways to factor a polynomial, and you will need to look for patterns to determine which kind of factoring can be done with different types of polynomails.  Today, we will look at the most basic type of factoring, but one of the most important - the greatest common factor.  This is the first kind of factoring that you should always look for.

Things you should be able to do after today:

  • factor a polynomial using the greatest common factor
  • factor a 4 term polynomial by factoring in groups
  • recognize when a greatest common factor of -1 needs to be used

Resources

  • Notes

Assignment

  • p220 #1-7ace #8-13, 16, *17, *18
Attachments:
FileDescriptionFile size
Download this file (10.5.2.notes.pdf)10.5.2.notes.pdf 3966 kB

Things you should be able to do after today:

  • multiply binomials x binomials
  • multiply binomials x trinomials
  • simplify expressions that combine multiplication and addition/subtraction of polynomials

Resources

  • Notes

Assignment

  • p209 #1, 2, 13, 14
  • p209 #3-4ace, #5, 6, 8, 10, 12, 15, 16
Attachments:
FileDescriptionFile size
Download this file (10.5.1a.notes.multiplying.binomials.pdf)10.5.1a.notes.multiplying.binomials.pdf 3388 kB
Download this file (10.5.1b.notes.multiplying.binomials.pdf)10.5.1b.notes.multiplying.binomials.pdf 3343 kB
   
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