f(x)=x3−2x2−3x+1
Minimum point: (-1,-6)
Maximum point: (3,4)
Domain: All real numbers
Range:(-∞,∞)
X-intercepts:(-1,0) and (3,0)
2x3-3x2+4x-6
x2(2x-3)+2(2x-3)
(2x-3)(x2+2)
Divide 2x3+5x2−3x+1 by x+2 using long division.
2x2-x+1 and the remainder is 11
9x2-16
(3x-4)(3x+4)
x3-8
(x-2)(x2+2x+4)
g(x)=x4−4x3+2x2+5x−2
Minimum point: (-1,-6)
Maximum point: (2,3)
Domain: All real numbers
Range:(-∞,∞)
X-intercepts:(-1,0) and (2,0)
x2-9
(x-3)(x+3)
divide 3x4-7x2+4x-2 by x-1 using long division
x3+x2+3x+2
8x3-27
(2x-3) (4x2+6x+9)
2x3+6x2+4x+8
(x+1)(x2+2)
h(x)=2x3+3x2-6x-4
Minimum point: (-2,-10)
Maximum point: (1,1)
Domain: All real numbers
Range:(-∞,∞)
X-intercepts:(-2,0) and (1,0)
x3+8
(x+2)(x2-2x+4)
Divide 4x5+2x4-5x2+3 by x+1 using synthetic division
4x4-2x3+2x2-3x+1 and the remainder is 6
x2+4=0
x=+-2i
x2+4x+4=0
x=-2i
k(x)=3x4-8x3+4x2+2x+1
Minimum point: (-1,-4)
Maximum point: (2,5)
Domain: All real numbers
Range:(-∞,∞)
X-intercepts:(-1,0) and (2,0)
x3-27
(x-3)(x2+3x+9)
Divide 2x3-4x2+7x-3 by x+3 using synthetic division
2x2-10x+1
27x3-64
(3x-4)(9x2+12x+16)
x3+27
(x+3)(x2-3x+9)
m(x)=x3-6x2+9x+4
Minimum point: (0,4)
Maximum point: (3,4)
Domain: All real numbers
Range:(-∞,∞)
X-intercepts:(0,0) and (3,0)
4x3-16x
4x(x2-4)
Divide 5x4+3x3-6x2+2 by x-2 using long division
x3+5x2+14x+30 and the remainder is 82
x4+4=0
x=+-√2i
x4+4x2+4=0
x=+-2i