Aim #48: How do we factor polynomials?
HW: Handout
Do Now: Factor 10a2 - 9a + 2.
Factor by Grouping
We can also use factor by grouping to factor polynomials that have 4 terms. This
method does not ALWAYS work so we must be careful and pay attention to the
details!
1. x3 + x2 + 5x + 5
2. 2x3 + 3x2 - 8x - 12
3. 4x3 - 12x2 + 2x + 2
4. x3 - 5x2 + 3x - 15
Factoring Higher Degree Trinomials
We can factor higher degree trinomials with many of the techniques we have
already learned as long as the structure of the polynomial is correct.
Factor the following:
1. x4 - 6x2 - 27
2. x4 + 6x3 + 9
Why is the first polynomial expression factorable but the second one is not?
Factor:
3. x4 + 6x2 + 5
4. 4x4 - x2 - 18
5. 2x6 - x2 - 3
6. x8 - 2x4 - 63
Practice: Factor the following polynomial expressions
1. xy + 2x + 3y + 6
2. x4 - 15x2 - 250
3. x3 + 3x2 - 64x - 192
4. 3x8 - 47x4 - 16
Let's Sum It Up!!
When factoring 4 term polynomials we must make use of factor by grouping. When
factoring higher degree trinomials we must first identify it has the right structure,
then factor with the same methods we used before!