3.1 polynomial graphs
is this polynomial in standard form?
4x3+2x6-8x+12
NO
2x6 should be first
add:
(3x3-x-3)+(2x3-2x+8)
5x3-3x+5
multiply:
(x+2)(x+1)
x2+3x+2
(x3+3x2+3x+1) divided by
(x+1)
x2+2x+1
what are the x-intercepts of this polynomial:
f(x)=(x)(x-5)(x+3)
zeros at x= 0 , 5 , and -3
What is the leading coefficient:
-x3+5x2-10
negative one
-1
add:
(8x3-2x2+1)+(x3-2x-8)
9x3-2x2-2x-7
multiply:
(2x+3)(x-1)
2x2+x-3
(2x3+4x2-6x-12) divided by
(x+2)
2x2-6
what are the x-intercepts of this polynomial:
f(x)=x3+7x2+10x
zeros at x= 0 , -2, and -5
What is the degree:
-6x5+2x3-x-14
five
5
subtract:
(5x3+4x+2)-(x3+2x+1)
4x3+2x+1
multiply:
(x2+3)(x-2)
x3-2x2+3x-6
(x3-20x-25) divided by
(x-5)
x2+5x+5
sketch the graph
f(x)= x(x+2)(x-4)
down to the left, up to the right
x-intercepts at 0,-2, and 4
What polynomial family (degree and leading coefficient) has the following end behavior:
down to the left
down to the right
as X approaches -inf. Y approaches -inf.
as X approaches +inf. Y approaches -inf.
EVEN degree
NEGATIVE leading coefficient
subtract:
(5x3-2x+10)-(x3-3x+2)
4x3+x+8
multiply:
(x2+3x+1)(x+5)
x3+8x2+16x+5
(2x3-4x2+12) divided by (x-3)
2x2+2x+6+30/(x-3)
if a polynomial does not cross the x-axis then what must be true about its solutions?
they are imaginary
{square root of negative values involved}
What is the end behavior of an odd (degree) negative (leading coefficient) graph?
up to the left
down to the right
as X approaches -inf. Y approaches +inf.
as X approaches +inf. Y approaches -inf.
subtract:
(-2x3+x-3)-(5x3-x-3)
-7x3+2x
multiply:
(x+1)(x+5)(2x-4)
2x3+8x2-14x-20
(4x3+2x2+10x+5) divided by (2x+1)
2x2+5
sketch the graph
f(x)= x(x+5)2(x-3)
up to the left, up to the right
x-intercepts at 0,-5, and 3
crosses at 0 and 3
touches at -5