Factoring
factor: y=x4+7x2+12
(x2+4)(x2+3)
f(x)=x3-56
right up
left down
f(x)=(x-1)(x+3)(x)
0, 1, -3
y=x3 -5x+8
cubic
x3-8
y=x6-5x3+4
both up
f(x)=x3-4x
0, 2, -2
y=x4-6x2
quartic
3x4+8x2-3
(3x2-1)(x2+3)
y=-x4-6x3+1
both down
f(x)=x4-3x2-28
sqrt(7). -sqrt(7), 2i, -2i
y=x2
quadratic
8x3+1
(2x+1)(4x2-2x+1)
y=-x5-7x2+10
right down
left up
x3+27
-3, (3+/-3isqrt(3))/2
y=2x-8
linear
y=x3-7x4+5x2
quartic