Synthetic Division
Set up synthetic division for the following equation:
x4 + 3x2 - 7x2 - x + 6 Divided by x + 2
-2 1 3 -7 -1 2
Given the equation x8 - 10x4 + 16 = 0, please identify the value of u.
u = x4
To clear a polynomial raised to a power, you must first multiply by a reciprocal to clear the ____________. Then, you can multiply by a reciprocal to clear the _________.
Options: Numerator, Denominator
Blank #1: Numerator
Blank #2: Denominator
The numbers that serve as a dividing line between solutions that satisfy a polynomial inequality and those that do not are called ________ _________.
Critical Numbers
Since dividing by 0 will result in an undefined answer, you cannot have a closed dot in the __________.
Options: Numerator, Denominator
Denominator
Reduce the following polynomial using synthetic division:
x5 + 6x4 - 11x3 - 84x2 + 28x + 240 Divided by x + 2
(x + 2)(x4 + 4x3 - 19x2 - 46x + 120)
Solve for the variable using u substitution:
x8 - 18x4 + 32 = 0
x = -2, 2, and the positive and negative fourth root of 2
Solve for the variable:
(x - 5)2/3 = 9
x = -22, 32
Solve and graph the following polynomial inequality:
c2 + c < 20
Solution: (-5, 4)
Graph: See the Board
Solve for x in the following rational inequality and graph the solution(s):
x - 6 / x + 5 > 0
Solution: (Negative Infinity, -5) or (6, Positive Infinity)
Graph: See the Board
Solve for the variable using synthetic division.
x3 - 9x2 + 26x - 24 = 0
x = 2, 3, and 4
Solve for the variable using u substitution:
x1/2 + 5x1/4 - 126= 0
x = 6,561 and 38,416
Solve for the variable:
(x + 10)3/2 = 125
x = 15
Solve and graph the following polynomial inequality:
x4 +10x3 - 11x2 (Less Than or Equal to) 0
Solution: [-11, 1]
Graph: See the Board
Solve for x in the following rational inequality and graph the solution(s):
x +5 / x - 13 > -x + 5
Solution: (7, 10) or (13, Positive Infinity)
Graph: See the Board