1. Special Cases in Factoring Polynomials
Chapter 10.5

2. Factoring Quadratic Binomials
49x2 – 25
The difference between two squares.
The two binomial factors will be the same except for the sign between terms.
The factors will be created by the square-root of each part.
The square-root of 25 is 5.
49x2 – 25
The square-root of 49x2 is 7x.
= (7x + 5)(7x – 5)

3. Perfect Square Trinomials
x2 – 12x + 36
The last term will be a perfect square.
The middle term will be twice the square-root of the last term.
The sign of both binomials is the same as the sign in front of the middle term.
= (x – 6)(x – 6)
= (x – 6)2

4. If you can, always factor out the GCF
18x2 – 200
GCF of 18x2 – 200
2 divides evenly into 18 and –200.
2(9x2 – 100)
The remaining binomial is a
difference of squares.
2(3x – 10)(3x + 10)
Remember, they will have different signs.

5. In your notebooks, factor the following:
1) x2 – 16x + 64
2) x x + 64
3) x2 – 64
= (x – 8)2
= (x + 8)2
= (x – 8)(x + 8)

6. Homework: pg 489 (5-20 all)