Factoring & Quadratic Patterns
Factor completely: 3x2+10x-8
(3x-2)(x+4)
Simplify
(6x2-8x+11) - (2x2-5x+15)
4x2-3x-4
Find all zeros of f(x) = x(x-4)(2x+3)2
x = 0, 4, -3/2
Simplify: (5-3i)-(-2+7i)
7-10i
Simplify: (x2-9)/(x2+5x+6)
(x-3)/(x+2)
Factor by grouping:
2x3-6x2+5x-15
(2x2+5)(x-3)
Multiply using the box method
(2x-3)(x2+4x-5)
2x3+5x2-22x+15
State the degree, leading coefficient, and end behavior of f(x) = -3x5+4x3-2x+7
Degree: 5
LC: -3
EB: as x approaches -inf, f(x) approaches inf; as x approaches inf, f(x) approaches -inf
Simplify: (4-2i)(3+5i)
22+14i
Multiply: (x2-4)/(2x+6) by (x+3)/(x-2)
(x+2)/2, where x cannot =-3,2
Factor using a quadratic pattern:
x4-13x2+36
(x-2)(x+2)(x-3)(x+3)
Divide:
(4x5+12x4-8x3+20x2) by (2x2)
2x3+6x2-4x+10
Determine if x-2 is a factor of P(x)=x3-3x2+4x-4 using the Remainder Theorem.
P(2)=0, so x-2 is a factor.
Calculate the discriminant of 3x2-6x+3=0 and describe the nature of its roots
Discriminant: 0 (1 real solution)
Divide: 3x2/(x2-16) by 9x/(x+4)
x/[3(x-4)], where x cannot = -4,0,4
Factor the difference of cubes:
x3-27
(x-3)(x2+3x+9)
Divide using long division
(x3-4x+6) by (x+4)
x2-4x+12+ -42/x+4
Find all real and complex roots of x3-8=0.
x=2, -1+i sqrt3, -1-i sqrt3
Solve using the quadratic formula: x2-6x+13=0
x=3 + 2i, 3 - 2i
Subtract: x/(x2-4) - 2/(x+2)
(-x+4)/[(x-2)(x+2)]
Factor the sum of cubes
8x3+125
(2x+5)(4x2-10x+25)
Use synthetic division to evaluate f(3) for
f(x) = 2x3-4x2+5x-9
f(3)=24
According to the Fundamental Theorem of Algebra, how many real and/or complex roots does f(x)=5x4-2x3+x-9 have?
4 roots
Solve: 3x2+12=0.
x= 2i, -2i
Solve for x: x/(x-2) = 2/(x-2) +3
No solution (x=2 is extraneous)