Factoring More Difficult Trinomials

1
Factoring More Difficult Trinomials

• Students will be able to factor other trinomials
  using the Bottoms Up method.

2
Factoring

• When the quadratic term (first one) has a
  coefficient other than 1, factoring becomes more
  difficult. These polynomials are in the form
  .
• We follow four steps to factor these polynomials

3
Steps for Bottoms Up

• Multiply the first coefficient and the last term
  together.
• Find the pair of factors that will combine to
  produce the middle term.
• Put each factor of the pair over a which is the
  leading coefficient and reduce the fractions.
• Use Bottoms Up to write the factors of the
  trinomial.

4
What is Bottoms Up?

• Once you have your two reduced fractions, how do
  you write the factors of the trinomial?
• Lets suppose these are your fractions
• Do the following
• becomes _____ and becomes
  ______

5
Example 1

• Multiply the first and last coefficients

2 x 20 40 We need to find a pair of factors of
24 that combine to give us 5
-1 and 40 -2 and 20 -4 and 10 -5 and 8
1 and -40 2 and -20 4 and -10 5 and -8
6
Example 1

• Multiply the first and last coefficients

4 x 6 24 We need to find a pair of factors of
24 that combine to give us 5
-1 and 24 -2 and 12 -3 and 8 -4 and 6
1 and -24 2 and -12 3 and -8 4 and -6
7
Example 2

• Multiply 8 x 15 120. Find all pairs of factors
  of 120. We need a pair that combines to 26.

1 and 120 2 and 60 3 and 40 4 and 30 5 and 24 6
and 20 8 and 15 10 and 12