Adding, Subtract, and Multiplying
(5x3 + 2x2 - 11) + (7x2 - 6x + 4)
5x3 + 9x2 - 6x - 7
(x2 + x - 2) ÷ (x - 1)
(x + 2)
Sketch the end behavior of f(x) = -4x3 + 2x2 - 3x + 12.
[picture]
The solutions to the factored function (x + 2)(x - 3)(x2)
x = -2, x = 3, x = 0
The behavior of the graph h(x) = (x - 2)2 (x + 3) at the x intercept of 2.
bounce
(6x2 + 5x + 4) - (3x2 - 4x + 8)
3x2 + 9x - 4
Image question - A
(3x3 + 4x2 - 5) ÷ (x + 2)
Sketch the end behavior of g(x) = -4x4 + 2x2 - 3x + 12.
[picture]
The solutions to the factored function g(x) = (x2 + 3)(x - 4)(x + 4)
x = 4, x = -4
The first factor has no solution.
The shape that a quadratic function makes on a graph
parabola
(x3 - 3x2 + 7) - (x4 + 2x3 + 8x)
-x4 - x3 - 3x2 - 8x + 7
Image Question - B
-13
For the function f(x) = 4x3 + 3x2 - 3x - 21, as x -> ∞, f(x) approaches this.
∞ (positive infinity)
factor x3 + 10x2 + 21x completely
x (x + 3) (x + 7)
The concert that Katherine has been saving all her $$$ for.
Beyonce
(2x + 5)(x2 + x - 1)
2x3 + 7x2 + 3x -5
The remainder when (x3 - 2x2 - 2x + 8) is divided by (x - 1)
5
For the function f(x) = -6x6 + 9x5 - 3x3 - 21, as x -> -∞, f(x) approaches this.
- ∞
Factor 5x7 - 125x5 completely.
5x5(x - 5)(x + 5)
The behavior of the graph g(x) = (x - 4)5 (x + 9) at the x intercept of 4.
Wiggle/squiggle/flatten out
(3x-2)3
27x3 - 54x2 + 36x - 8
Is (x - 1) a factor of (x4 + x3 - 25x2 - 37x + 60) ?
Yes! When we divide the polynomial by (x - 1), the remainder is 0.
Sketch the end behavior for the function represented by k(x) = (x - 2)(x+3)(x - 4)2
[drawing]
Factor completely: m(x) = 8x3 + 27
(2x + 3)(4x2 - 6x + 9)
To factor a binomial a3 - b3, use this formula.
(a - b)(a2 + ab + b2)