Download Notes for Factoring Trinomials Using Bottoms-Up

Notes for Factoring Trinomials Using Bottoms-Up
Today, we will factor trinomials that have a number in front of
Example:
by using a method called Bottoms-Up
We will follow the same process we used before to factor a trinomial, but we will add one more step at the
beginning and one more step at the end.
To Factor a Trinomial into 2 Binomials when there is a leading coefficient:
1. Always look for and factor out the ____Greatest Common Factor____(_GCF_) first if there is one.
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Example:
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2. __Multiply__ the coefficient of the __first__ term by the __last__ term, and write a new trinomial with
as the first term, the same middle term, and the product of the multiplication as the last term.
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Example:
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3. When the first term of trinomial is , you can factor like we did before. The first term in each set of
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parenthesis will be . So, go ahead and write out (
Example:
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4. Find 2 numbers that _multiply_ to give you the _last_ term and _add_ to give you the _middle_ term.
a. Look at the last term of the trinomial, and write down each pair of factors that multiply to give the last term.
*Note:
If the last term is _ positive___ you are looking for 2 factors that have the __same__ sign as the middle term.
If the last term is _negative___ you are looking for 2 factors that have _ different__ signs.
b. Add each pair of factors together, and pick the pair of factors that add to give you the middle term.
Example:
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-15 = -16
-5 = -8
5. Now, since we multiplied by the leading (first) coefficient (in this case __3__) in the beginning, we have to
_divide_ each number in our parenthesis by that number to get our actual answer.
When you divide, if the number can be divided nicely, then do it. If the number does not divide nicely, then
you Bottoms-Up…bring the number on the bottom up in front of x (inside the parenthesis not outside).
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Solution:
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6. You can always check your factoring by __multiplying__ it back out to match the original trinomial.
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(Practice problems are on the back.)
Math Models – Fletcher 2012-2013
Practice: Factor completely.
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