Intro to Polynomials
What is the degree and leading coefficient of
f(x)=3(x2-3)(x+4)
degree = 3
Leading coefficient=3
(x2-6x+2) + (5x2-x-8)
6x2-7x-6
2x2-5x-3
(x-3)(2x+1)
What is the formula for finding the rational zeros?
P = Factor of a0
___________________
Q Factor of an
How many zeros
f(x)= 3x3+2x2-4x+1
3 zeros
What is the degree and leading coefficient of
f(x)=3x2-3x+6
Not a polynomial
(8x-3+9x3) - (x3-13x2-4)
8x3+13x2+8x+1
5x5-80x3
5x3(x-4)(x+4)
List the possible zeros
f(x) = x3-4x2-15x+18
p= +_ 1,2,3,6,9,18
q= +_ 1
How many zeros are there and what are they?
f(x)=(x-3)(x+4)2(x+6)4
x=3
x=-4 repeated twice
x=-6 repeated 4 times
Evaluate the function
f(x)= 4x3-3x2+2x-1 at x=2
f(2)=23
(4x2-2+1)(x-2)
4x3-8x2-x+2
x3+y3
(x+y)(x2-xy+y2)
find all zeros
f(x)= x3-8x2+5x+14
-1, 2, 7
How many solutions will this equations have
f(x)=(x2-4x+1)3(x+1)2
8 solutions
Describe End Behavior?
What is the behavior of the graph as z approaches positive and negative infinity
(x-5)(x+6)(x+2)
x3+3x2-28x-60
Divide using synthetic division
f(x)=3x3+17x2+21x-11 by g(x)= x+3
3x2+8x-3+ (-2/x+3)
find the zeros of
f(x)= 48x3+4x2-20x+3
x= 1/2
x= -3/4
x=1/6
How many rational zeros and what are they
f(x)= x3-9x2+6x-1
x=1
x=1
x=2
x=1/4
What is the end behavior of
f(x)=-7x5+5x3-12x+12
limf(x) =-infinity when x is going towards + infinity
limf(x)=+infinity when x is going towards - infinity
(y+5)3
y3+15y2+75y+125
27x3+45x2-3x-5=0
x=-5/3, 1/3, -1/3
f(x)=5x3+29x2+19x-5
x=-5, -1, 1/5
How many zeros and what are they?
f(x)=2x3+9x2+19x+15
x= - 3/2