X, +, - polynomials
(3x2 + 5x + 2) +( 2x2 -x + 7)
5x2 + 4x + 9
Synthetic division: (2x2 - 9x - 5)/(x - 5)
2x+1
Use Descartes rule of signs to determine the possible positive negative and imaginary zeros.
f(x)=5x3 - x2 + x + 6
+: 2 or 0
-: 2 or 0
imaginary: 3 or 1
See my computer for graph.
Expand (x - 2)4 using Pascal's triangle.
x4 - 8x3 + 24x2 - 32x + 16
(4x3 - 2x + 1) + (7x2 + 12x)
4x3 + 7x2 + 10x + 1
Long division: (x2 + 5x + 6)/(x + 2)
x+3
Use Descartes rule of signs to determine the possible positive negative and imaginary zeros.
f(x)=2x5 + 3x4 - 2x3 - 12x2 + x + 4
+: 2 or 0
-: 3 or 0
imaginary: 4, 2, or 0
Solve using possible solutions and synthetic division f(x)= x3 - 2x2 - 5 + 6
x= 1, 3, -2
Find the polynomial function f(x) of least degree that has rational coefficients, a leading coefficient of one, and the zeros 3 and 2 + root 5
f(x)= x3 - 7x2 + 11x + 3
(4x2 - 3x + 7) - (7x2 + 2x - 5)
-3x2 - 5x + 2
Synthetic Division: (2x2 - 4x + 3)/(x + 6)
2x-16 remainder: 99/(x + 6)
Use the rational root theorem to identify all real possible solutions.
f(x)= x3 - 5x2 + 4x + 24
p/q= positive or negative 1, 2, 3, 4, 6, 8, 12, 24
Solve using possible solutions and synthetic division
f(x)= x3 - 2x2 - 2x+ 4
x= positive or negative root 2, 2
Expand (2x + 6)5 using Pascal's triangle
3x5 + 480x4 + 2,880x3 + 8,640x2 + 12,960x + 7,776
(x + 3)(x - 4)
x2 - x - 12
Synthetic division: (5x3 - 2x + 5)/(x + 4)
5x2 - 20x + 78 remainder: -307/(x + 4)
Use the rational root theorem to identify all real possible solutions.
f(x)= 3x4 - 4x3- 14x2 + 24x + 12
p/q= positive or negative 1, 1/3, 2, 2/3, 3, 4, 4/3, 6, 12
If you have a rectangular container with dimensions 2x + 1, x + 3, and x + 2, what is the expression of its volume?
2x3 + 11x2 + 17x + 6
Find the polynomial function f(x) of least degree that has rational coefficients, a leading coefficient of one, and the zeros 4 and 2 + i
f(x)= x3 - 8x2 + 19x - 12
(2x - 1)(3x2 + 4x - 5)
6x3 + 5x2 - 14x + 5
Long Division: ( 2x3 + 6x2 + 4)/(x2 - 2)
2x + 6 remainder: (4x - 8)/(x2 - 2)
Use Descartes rule of signs to determine the possible positive negative and imaginary zeros and Use the rational root theorem to identify all real possible solutions.
f(x)= x3 - 5x2 - 4x + 15
p/q= positive or negative 1, 3, 5, 15
+: 2 or 0
-: 2 or 0
imaginary: 3 or 1
You were trying to find the dimensions of a pool that has a volume of 2x3 + 16x2 + 42x + 36. You know two of its dimensions: x + 3 and x + 2. What is the third dimension?
2x+6
Graph 4x4 - 2x3 - 12x2 - 2x + 4
include the factored form, degrees of freedom, whether it's even or odd, and the zeros including the multiplicities.
See my computer for graph and info.