MCR3U – Rational Expressions
533571610
Date: _________________________
Factoring Complex Trinomials
Recall - a monic trinomial has an 'a' value of 1.
When factoring always check for a common factor first!
To Factor complex trinomials we use a method called Decomposition.
Decomposition: (definition)
 to breakdown,
 the state of being reduced into original elements,
 breaking down a process into sub processes and activities
To factor complex trinomials the first step is the same - we still need to find two integers
that add to 'b' and multiply to 'ac' but the process that follows that step is somewhat
more complex.
Example: 3x 2  5x  2
Here, we need to find two numbers that add up to ___ and multiply to ___.
Once you have found the two integers, to factor the complex trinomial:
Use the integers to break up the middle term (the 'b' term)
If we are factoring properly, as this step, we should always get two identical brackets.
Factor by grouping - common factor the first two terms and common factor the last two
terms:
Example:
6x 2  7x  5
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MCR3U – Rational Expressions
533571610
Examples:
12x 2  11x  5
8x 2  10x  3
6y 2  19y  15
10x 2  22x  4
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