Classifying Polynomials
quadratic trinomial
4x3-3x
down and up
3x2-4x+2
1 turning point
3x3-5x2+12x
x(3x2-5x+12)
3x2+2x−9=6x−10
x=1 x=1/3
5
constant monomial
down and down
4x4-2x3+7
3 turning points
3x2+12x-6
3(x2+4x-2)
4x2+12x=4x-3
x=-1/2 x=-3/2
6X5-2x4+7x3+x2-8x-3
quantic polynomial of 6 terms
up and down
x7+5x6+3x-1
6 turning points
4x3+16x2-8x
4x(x2+4x-2)
3x2+10x+2=−6
x=-4/3 x=-2
6X3+4
cubic binomial
7x2+6x-1
up and up
x4+3x-1
3 turning points
64x2-24x-16
8(8x2-3x-2)
3x2+5=5x+7
x=-1/3 x=2
x4+3x3-6x2
quartic trinomial
-4x4+3x2+4
down and down
3x8-8x6+3x5-7x+1
7 turning points
15x2-30x+40
5(3x2-6x+8)
5x2+9x=7x+7
x=-7/5 x=1