B.4 Review of Factoring
Factoring is to write a polynomial as a _____________
of two or more nonconstant polynomials.
Common
Factor
3x 4 + 6x 3 -12x 2 = 3x 2 (x 2 + 2x - 4)
Difference of
squares
x 2 - a2 = (x - a)(x + a)
Trial and
error
Difference of
Cubes
x 2 + 2x - 3 = (x + 3)(x -1)
x 3 - a3 = (x - a)(x 2 + ax + a2 )
Sum of Cubes
x 3 + a3 = (x + a)(x 2 - ax + a2 )
Grouping
x 3 - x 2 + x -1 = (x 3 - x 2 )+ (x -1)
= x 2 (x -1) + (x -1)×1
= (x -1)(x 2 +1)
1
Ex1: 121x - x 3
Ex4: (x +1)-1/2 - (x +1)-3/2
Ex2: 1000 - 8x 6
Ex5: x 3 + 3x 2 + 3x +1
Ex3: x 8 -1
Ex6: x 4 - 2x 3 - 6x 2 + 7x +10
2
Ex7: 4x 2 + 4xy + y 2 - c 2 + 4c - 4
Ex9: (x + y)2 + (x + a)2 - (a + b)2 - (y + b)2
Ex8: 4x 2 -12xy + 9y 2 - 20x + 30y + 25
3
Ex10: (b - c)3 + (c - a)3 + (a - b)3
Ex11: 12 x -1/2 (3x + 4)1/2 - 23 (x)1/2 (3x + 4)-1/2
4
Ex12: nx 4n + 2nx 2n y 2n + ny 4n
Ex13: (a2 + 2a)2 - 2(a2 + 2a) - 3
5