Download Factoring Lesson

4
5x
– 405
= 5(x4 – 81)
= 5(x2 + 9)(x2 – 9)
=
2
5(x
+ 9)(x + 3)(x – 3)
by D. Fisher
Modified by R. Lindsey
• Factors are numbers, variables,
expressions that are multiplied.
• Factoring starts with a product and
finds the factors.
• Prime numbers have factors of only
themselves and 1.
• Prime factorization breaks products down to
prime factors. Ex: 6 = (2) (3)
10 = (2) (5)
30 = (2) (3) (5)
40 = (2) (2) (2) (5)
2
3x y
+ 12xy
= 3xy(x + 4)
3
x
=
+
2
5x
2
x(x +
–x
5x – 1)
2
x
– 81
= (x + 9)(x – 9)
2
4x
– 121
=
(2x + 11)(2x – 11)
2
x
– 14x + 49
= (x –
2
7)
2
x
+ 8x + 16
= (x +
2
4)
2
25x
– 10x + 1
= (5x –
2
1)
2
x
+ 10x + 16
= (x + 8)(x + 2)
2
x
+ 4x – 21
= (x + 7)(x – 3)
2
2x
+ 7x + 3
= (2x + 1)(x + 3)
2
x
–x–6
= (x – 3)(x + 2)
2
3x
=
+24x + 21
2
3(x
+ 8x + 7)
= 3(x + 1)(x + 7)
4
x
=
2
(x
2
(x
+
– 16
2
4)(x
– 4)
+ 4)(x – 2)(x + 2)
2
xy
+4xy + 4y
= y(x +
2
2)
2
9x
+ 6x + 1
= (3x +
2
1)
2
2x
– 18x + 40
= 2(x – 4)(x – 5)