Classifying polynomials and End behaviors
Name the polynomial example by degree 4x3-2x2+x
cubic
In what form should this equation be in? x3-2x2-15x
factored form
Name 2 of the 6 factoring techniques
factoring the GCF, Difference of squares
Name the two ways to solve using long division
Numerical long division and Polynomial long division
If 3-2i and 5/2 are roots of P(x)=0 what is the other root?
3-2i=3+2i
Give a polynomial example with 4 terms and name the degree
-x5+4x2+2x+1 number of terms 4, fifth degree
What are the zeros of y=(x+2)(x-1)(x-3)?
x=-2, x=1, x=3
what are the real or imaginary solutions for each polynomial expression x6-16x2=0
x=0, x=+-2i, x=+-2
use long division to find the quotient and remainder of 4x2+23x-16 by x+5
quotient 4x+3; remainder -31
The roots of a cubic are -2 and 4i. solve in standard form
P(x)=x3+2x2+16x+32
write the polynomial in standard form and classify the degree and terms...3x+9x2+5
9x2+3x+5;quadratic trinomial
name the zeros and the multiplicities for each zero of y=(x-6)2(x+2)
zeros--x=6;x=-2; multi of 2(bounce), multi of 1 (cross)
x4=16
x=+-2i
use synthetic division to solve 2x3+x2-7x-6=0 (use calculator to find real zero)
x=2,-3/2,-1
Find the 3rd term of (x-2)5
10(x)3(-2)2=40x3
what is the end behavior of each graph? y=-7x4+8x6-2
a=8;n=6; 6-1=5; Max t.p. up and up
find the relative max and minimum of the graph f(x)=x3-x2-9x+9
relative max=16.9; min=-5.05
what are the real solutions of the equation (use calculator) x3+x2=x-1
x=-1.84
solve 15x3-32x2+3x+2=0 (use calculator)
x=+-1/3, 2
Use descartes Rule of signs to solve 2x4-x3+3x2-1=0 name the sign changes
There is one sign change, so one negative real root
what is the end behavior of each graph? Include the max # of t.p; y=-2x4+8x3-8x2+2
leading term -2x4; a=-2 n=4; down and down max t.p 3
The volume of a box is x3-3x2+3x-1 cubic units. Explain how to find the length of a side if the box is a cube.
The factors of this polynomial are (x-1), (x-1), (x-1), bc all 3 factors are equal and the sides of the box are equal, the side length would be x-1
solve (x2-1)(x2+4)=0
4i/2+-2i
If the polynomial x3+6x2+11x+6 expresses the volume, in cubic inches, of the box, and the width is (x+1) in. What are the dimensions of the box
x2+5x+6=0--(x+3),(x+2)
L=x+2, H=x+3
what are the rational roots of each polynomial equation? 3x3+7x2+6x-8=0
x=1,-1,8,-8,2,-2,4,-4,1/3,-1/3,8/3,-8/3,2/3,-2/3,4/3,-4/3
one root:x=2/3