Polynomial Operations
(3x2 + 5x - 2) + (-2x2 - 2x + 2)
x2 + 3x
Find the zeroes of y = (x-3)(x+1)(x)
Which direction will the range of the graph of
y = -x3 +3x - 1 go towards as x gets larger and larger?
y will go towards negative infinity
Expand (x+5)2
x2+10x+25
What is the maximum number of turns the polynomial
y = 3x5+4x6-2x+1 can have?
Maximum of 5 turns (degree = 6)
(2x - 7x2 + 5 - 2) - (3x3 + 7x2 - 7)
-3x3-14x2+2x+10
Find the zeroes of y = x2 - 8x + 15
What happens at the zero of -1 of the polynomial
y = (x+1)2(x-1)3?
The graph turns around (even degree)
Expand (x+3)3
x3+9x2+27x+27
What is the end behavior of the polynomial
y = -5x4?
As x -> infinity, y -> negative infinity
as x -> negative infinity, y -> negative infinity
(graph is going down on the y-axis as you go both further left and right on the x-axis due to negative L.C. and even degree)
(2x2 - 3)(2x2 + 3)
4x4-9
Find the real zeroes of y = (x6-27)
-sqrt(3), sqrt(3)
Because f(x) = -f(x) f(2) = 8 and f(-2) = 8
Expand (x - y)3
x3-3x2y+3xy2-y3
Is the function y = |x -2| odd, even, or neither? Show algebraically
(x2+14x+38) divided by (x+8)
(x+6) R -10
Find the zeroes of y = 2x3-8x
x = -2, 0, 2
Write a polynomial that goes through the zero of 2, and turns around at the zeroes of 0 and -3
e.x. (x-2)(x)2(x+3)4
What is the the fourth term in the expansion of
(4y + x)4?
16x3y
Is (x - 1) a factor of x2-7x+10? Why or why not?
No, remainder of 4 when you divide
4x2-33 divided by (7x + 7)
6x - 6 R 9
Find all the zeroes of y = x3+9x2+23x+15 if (x+5) is a factor.
x = -1, -3, -5
Factor the polynomial (27x6+125)
(3x2+5)(9x4-15x2+25) -> sum of cubes
What is the coefficient of x3y2 in the expansion of
(x - 3y)5?
90
If a polynomial P(x) is divided by a factor (x + 2) and shows a remainder of 0, what does the Remainder Theorem tell us we should expect when we evaluate P(-2)?
P(-2) should also = 0