Factoring
Factor: x2 + 6x - 27.
(x - 3)(x + 9)?
The standard form polynomial function with zeros 4, 0, 1.
f(x) = x3 - 5x2 + 4x
Is (x-2) a factor of P(x) = x3 + 2x2 -6x - 4? Show why or why not.
Yes; P(x) = (x - 2)(x2 + 4x + 2)
Find all zeros:
f(x) = 2x4 + 3x2 + 1
-1/5, -1, -1
f(x) = x3 - 5x2 + 6x - 6; find f(3)
f(3) = -6
Factor: 2x3 + 36x2 +160x.
2x(x + 8)(x + 10)?
The standard form polynomial function with zeros -2, 2, 3.
f(x) = x3 - 3x2 - 4x + 12
Find all zeros:
f(x) = x3 + 7x2 + 10x.
{0, -2, -5}
Find all zeros:
f(x) = x3 - 2x2 + 10x + 136
{-4, 3+5¡, 3-5¡}
f(x) = x3 - 5x + 5; find f(2)
f(2) = 3
Factor: 16x3 - 2x2 + 56x - 7.
(2x2 + 7)(8x - 1)?
The standard form polynomial function with zeros 1, 2, 5/4.
f(x) = 4x3 - 17x2 + 23x - 10
Find all zeros:
f(x) = x4 - 40x2 + 144.
{-6, 6, -2, 2}
Find all zeros:
f(x)= x3 - 216
{6, -3+3¡√3, -3-3¡√3}
f(x) = -2x3 + 17x2 - 33x + 30; find f(6)
f(6) = 12
Factor: 250x3 + 432
2(5x + 6)(25x2 - 30x + 36)?
The standard form polynomial function with zeros -4/3, -1/5, 2/5.
f(x) = 75x3 + 85x2 - 26x - 8
Find all zeros:
f(x) = 2x3 - 3x2 - 3x + 2
{-1, 1/2, 2}
Find all zeros:
f(x) = -x3 - x2 - 7x - 7
{¡√7, -¡√7, -1}
f(x) = x4 + 3x3 - 8x - 16; find f(-2)
f(-2) = -8
Factor: 20x8 - 21x4 + 4
(2x2 - 1)(2x2 + 1)(5x4 - 4)
The standard form polynomial function with zeros -3/5, -2i.
f(x) = 5x3 + 3x2 + 20x + 12
Find all zeros:
f(x) = 4x3 - 3x2 - 8x + 6
3/4, +- radical 2
Find all the zeros:
f(x) = 2x3 + 2x2 - 19x + 20
{3+¡/2, 3-¡/2, -4}
f(x) = -5x5 + 26x4 -9x3 + 20x2 + 5x - 17; find f(5)
f(5) = 8