Simplifying Expressions
(6x^3 + 7x^2 - 5) + (2x^2 - 13x - 12)
6x^3 + 9x^2 - 13x -17
9x^2 + 3x
3x(3x + 1)
Find the zeros and multiplicities:
x^2(x-1)^7(3x-5)^11
x = 0 *2
x = 1 *7
x = 5/3 * 11
x^2 + 8x + 15 = 0
x = -3, -5
f(x) = x + 3 , g(x) = x^2 - 3x + 1.
Find (f+g)(x).
x^2 -2x +4
(8x^4 + 2x^2 - 7) - (x^4 + 3x^3 - 2x^2 + 9)
7x^4 - 3x^3 + 4x^2 - 16
3x^2 -243
3(x+9)(x-9)
Is the function even or odd? Positive or negative?
The end behavior of my function falls to the left, and rises to the right.
Odd, positive
3x^4 - 48x^2 = 0
x = 0, 4, -4
f(x) = x^2 + 4 , g(x) = x-3.
Find (f*g)(x)
x^3 - 3x^2 +4x - 12
(x^2 + 4)^2 - 2x(x-4)
x^4 + 6x^2 + 24
2x^3 - 2x^2 - 60x
2x(x-6)(x+5)
Find the domain, range, rel min/max, inc/dec interval, and end behavior of the function.
f(x) = x^3 + 6x^2 - 12x + 1
Zeros: -7.6, 0.1, 1.5
Inc Int: (-inf, -4.83) , (0.83, inf)
Dec Int: (-4.83, 0.83)
Rel Max: (-4.83, 86.3)
Rel Min: (0.83, -4.25)
Dom/Ran : ARN
End Behavior: falls left, rises right
25x^2 = 49
x = 7/5, -7/5
f(x) = x^2 - 2x - 63 , g(x) = x+7.
Find (f/g)(x)
x - 9
(3x - 5)(x^2 + 12x - 5)
3x^3 + 31x^2 - 75x + 25
27x^3 + 64
Sum of cubes:
(3x+4)(9x^2 - 12x + 16)
Find the domain, range, rel min/max, inc/dec interval, and end behavior of the function.
f(x) = -x^4 -3x^2 + 12x
Zeros: 0 , 1.86
Inc Int: (-inf, 1.1)
Dec Int: (1.1, inf)
Rel Max: (1.1, 8.1)
Rel Min: none
Dom/Ran : ARN
End Behavior: falls left, falls right
9x^4 - 243x = 0
x = 0, 3, (-3 + i(rt27))/2, (-3 - i(rt27))/2
f(x) = x^3 + 3x^2 - 5 , g(x) = -x^2 + 32x - 15
Find (f o g)(3).
388,795
(22x^3y^2 + 38x^2y - 14x) / (2x^2y)
11xy + 19 - 7/(xy)
6x^3 - 5x^2 + 30x - 25
Factor by grouping:
(x^2 + 5)(6x-5)
Write the standard form of the graph that has zeros of 0 (multiplicity 2), -1 (multiplicity 2), and 1/2 (multiplicity 1).
x^5 + (3/2)x^4 - (1/2)x^2
3x^3 - 21x^2 + 7x - 49 = 0
x = 7, i(rt(7/3)), -i(rt(7/3))
(7x^3 - 18x^2 + 11x -13) / (x-5)
7x^2 + 17x + 96 + 467/(x-5)