Sum and difference of a square
(a + b)(a - b) = a2 + b2
2x2 - 20x2
2x2(x-10)
F(x) = -14
Constant
X2 + X2
2X2
(2x-5)(X + 4)
2x2 + 3x - 20
Cube of a binomial
(a + b)3 = a3 + 3a2b + 3ab2 + b2
3x2 - 27x - 30
3(x-10)(x+1)
F(x) = 5x - 7
Linear
X5 divided by X2
X3
(X+3)(X + 3)
X2 + 6x + 9
Vertex formula
-b/2a
2x2 + 28x + 96
2(x + 8)(x+6)
F(x) = 2x2 + x - 9
Quadratic
X5 times X3 times X9
X17
(X + 2)(3x2 - x - 5)
3x3 + 5x2 - 7x - 10
Sum of two cubes
a3 + b3 = (a + b)(a2 - ab + b2)
Is a2 + ab + b2/4 equivalent to (a + b/2)2
Yes
F(x) = x3 - x2 + 3x
Cubic
X9 + X5 - X3
X
(8x-3)2
64x2 - 48x + 9
Difference of two cubes
a3 - b3 = (a + b)(a2 + ab + b2)
6x2 + 72x + 192
6(x+4)(x+8)
F(x) = x4 + 2x - 1
Quartic
2X2 + 5X2
7x2
(3x+4)(3x-4)
9x2 - 16