Binomials
Factor completely: m3 + 27
(m + 3)(m2 - 3m + 9)
Factor completely: n2 + 2n +1
(n + 1)2
Factor completely:8xy + 3x + 48y + 18
(x + 6)(8y + 3)
Identify the rational zeros of f(x)= x2 - 6x + 5. Identify the multiplicity of the root/s (single, double, etc.)
Two rational zeros at x=1 and x=5 (both single roots)
Find the GCF of: 13a + 20b
GCF = 1
Factor completely: 2x4 - 54x
2x(x - 3)(x2 + 3x + 9)
Factor completely: 3x5 + 35x3 + 72x
x(3x2 + 8)(x2 + 9)
Factor completely: 2n3 + 4n2 + n + 2
(2n2 + 1)(n + 2)
Find the rational zeros of f(x)= x4 + 6x3 + 25x2. Identify the multiplicity of the root/s (single, double, etc.)
One rational zero at x=0 (double root)
Find the GCF of: 8x2 + 10x
GCF = 2x
Factor completely: 28n2 - 7
7(2n + 1)(2n - 1)
Factor completely: -40x2 + 244x - 24
-4(x - 6)(10x - 1)
Factor completely: 240ab + 40a2 - 150b - 25a
5(8a - 5)(6b + a)
Find the rational zeros of f(x)= x3 - x2 - 5x - 3. Identify the multiplicity of the root/s (single, double, etc.)
Two rational zeros at:
x= -1 (double)
x= 3 (single)
Find the GCF of: -15d5 + 45d3 - 60d2
GCF = -15d2 or 15d2
Factor completely: 216x6 + 343y6
(6x2 + 7y2)(36x4 - 42x2y2 + 49y4)
Factor completely: x8 + x4 - 90
(x4 + 10)(x2 + 3)(x2 - 3)
Factor completely: 2ab - 10b - 4a + 5b2
(2a + 5b)(b - 2)
For the function f(x)= 3x4 - 14x2 + 8,
1. find the rational roots
2. use synthetic division to factor into linear and irreducible quadratic factors
1. rational zeros at x=-2 and x=2
2. f(x)= (x - 2)(x + 2)(3x2 - 2)
Find the GCF of: 315mn2 - 504m2n - 588mn4
GCF = 21mn
Factor completely: 64x6 - y6
(2x + y)(2x - y)(4x2 + 2xy + y2)(4x2 - 2xy + y2)
Factor completely: 64x2 + 112x + 49
(8x + 7)2
Factor completely: 16x3y3 - 120x2y2p2 + 96x3y2p - 20x2y3p
4x2y2(4x - 5p)(y + 6p)
For the function f(x)= x4 + 5x3 + 4x2 + 20x,
1. find the rational roots
2. use synthetic division to factor into linear and irreducible quadratic factors
1. rational roots at x=0 and x= -5
2. f(x)= x(x + 5)(x2 + 4)
Find the GCF of: 24a3c2 + 60ac3 + 48acb2 + 36acb
GCF = 12ac