Factor Difference of Squares
8-5 page 109, # 1
x2 – 81
When the last term is negative,
what are the signs?
Both positive? Both negative?
Mixed?
(+)(+)
(-)(-)
(+)(-)
8-5 page 109, # 1
Difference of two squares
x2 – 81
The last term is negative,
so the signs are mixed.
Mult to 81; subtracts to 0.
(x+9)(x-9)
8-5 page 109, # 1
Difference of two squares
x2 – 81
Easier Way
Make signs mixed
Square Root each term
(x+9)(x-9)
8-5 page 109, # 1
Difference of two squares
x2 + 81
Cannot factor.
has + (sum)
If it had a minus, it would factor.
8-5 page 109, # 4
Difference of two squares
36x2 – 100y2 GCF: 4
Make signs mixed
Square Root each term
4(9x2 – 25y2 )
4(3x+5y)(3x-5y)
8-5 page 109, # 12
Difference of two squares
8y2 – 200 GCF:8
8(y2 – 25)
Mixed signs; square roots
8(y+5)(y-5)
8-5 page 109, # 10
Difference of two squares
- 81 + a4 GCF: none Flip around
a4 – 81
Mixed signs; square roots
(a2+9)(a2-9) factors more
(a2 + 9)(a + 3)(a – 3)
Factor Trinomials
8-5 page 109, # 21
3x4 + 6x3 – 3x2 – 6x GCF:3x
x3 + 2x2 – x – 2 = 0
Group them
(x3 + 2x2)+(– x – 2) = 0
x2(x + 2) – 1(x + 2) = 0
(x2 – 1) (x + 2) = 0
Factor Trinomials
8-5 page 110, # 1
81x2 = 49 set equal to 0
81x2 - 49 = 0
Difference of two Squares
(9x + 7)(9x – 7) = 0
Factor Trinomials
8-5 page 110, # 4
1x2 = 25 set equal to zero
4
1x2 – 25 = 0
4
Next mult by denominator
Factor Trinomials
8-5 page 110, # 4
1x2 – 25 = 0 set equal to 0
4
mult by denominator
x2 – 100 = 0
(x + 10)(x – 10) = 0
Factor Trinomials
8-5 page 111, # 1
x2 – 16x + 64
Same Signs: both negative.
(x – 8) (x – 8)
(x – 8) 2
Factor Trinomials
8-5 page 111, # 2
m2 + 10m + 25
Same Signs: both positive.
(m + 5) (m + 5)
(m + 5) 2
Factor Trinomials
Prime: cannot factor
x2 + 10x + 3
Same Signs: both positive.
But what mult to 3; adds to 10?
Nothing
1 times 3 = 3 but 1 + 3 = 4
Prime; does not factor
Prime Trinomials
Not everything factors
x2 + nx + 8
8 x 1; 8+1; 4 x 2; 4 + 2;
Only factors if middle term is 9 or 6.
x2 + 9x + 8 = (x + 8)(x + 1)
x2 + 6x + 8 = (x + 4)(x + 2)
x2 + 3x + 8 = Does not factor (Prime)