Chapter 5 Quiz. Review Part
I (No Granhine
Name:
Per:
Calculator)
1) Rewrite each polynomial
in standard form, classifii by:Jegree (quadratic, cubic, quartic, quantic, etc.) and classifu by the number of terms (binomial, trinomial, potynomiai). Polynomial
Rewrite in Standard X'orm
! :5x3 - xa !=x2*7-x y=].Ox+xs
Classify by # of terms
Desree
&wr.hr:
Binnrnin
U=XLX+I
(lunArah'c
Trinamial
-aX'o X'- |Xt 8 u= x5+bx
ruhiC
hlu nnrninl
Au,*hr
Btnomial
.Ul=-Kq
!=x2+B-4x-2x3
|
Classiff by
5N3
q--
I
2) Determine the end behavior based on the degree and the leading coefficient. Leading Coefficient
:(-rl- 2r' * r J(-r) :(5-d * ?;ul - .x * I !lx')
,f(.rJ:Sx3-9.r
fr1l :t1L$ .f(.r)
l[r) :
6,11
n
* _r *
3
-.:rr(jr - 1)'(* +21 (.r + 3){-r: + XJ"(.x +
l, t
4)
.lxwt) t
3) State each zero and its' multiplicity. Determine whether the graph will bounce on, wiggle through, or cross urrougn (xthrough each eacnzero zero (x-mIercepl ).
) YfinP(
Zeros
-/J -
f(x):@+g(x-L),
,f (x)
-
x2(x -
l5(x + 2)a(x -
1"0)
o
3
*e IO
wtultiolicitv
)r
)e
B,
W, or
C?
)c4
TB ,8
)tr) 7B
)c
,
i,
4) Factor each polynomial. State the zerds, tlreir multiplicities, and whether the graph bounce, wiggle, or cross through each zero (x-intercept).
a. f(x) -2x3
will
-t\xz +12x i \
A)r
$z-sx+ b)
,x (x-)fx-a) Multiplicitv
Zeros
Factored Form
o4
Sm=ar[x-t(x-O l
b. f (x) -
x3
€,
)r
C-- -l-)l
B,
W, or
C?
C
C C.
-9x
x (x'-q)
x(\*=)( x-3) Factored Form
Zeros
-)l tt
O
{fx)=r Uoz)U,
Multiplicitv
*3
3-- +l
5) Suppose a polynomial has the zeros: x = -2,7,4 a. Write the polynomial function iqfactored form.
+(D = (xn4f,x-D(x* q) b.
Write the polynomial function in standard form. Show your work.
*FCIL---..J._,
+fx)=(N"+x*O(x-q) '/ dis+rlburhve praperu4 "*r-/'
:,:Ti:"n[^? ffD=
lz-qA.n1a
fD=x
uffi
''
B,
W, or
o
C C,
C?
n! -
- 2)(x- 1) to answer the following questions. a.whatarethex-intercepts? X= 4, ,X= - U t= 8, t = I i:dlt CmgE) b. what is they-intercept? (plug inx:0) (- q)( l)f- a)C- l) = - 8
6) Use the functio
(x - 4)(x + 1)(x
c. What is the end-behavior?
t f
d. Sketch a graph of the function.
ktw',**,|fn*
ffiHffi s-"qJ
soLn
ff;:t&"'es 7) Write an equation infactoredform for each polynomial graph. Assume each tick mark on the x-axis represents 1 unit.
(x):
(x*D(x-Y nrd.o,tt
dlrsnlt
maJ*e l/
8) Find the real and imaginary solutions.of the equation by factoring.
a. x3*64=0
f,='t!
X3*{3
(X*q)(xlLl x + l&)=C Xt9=D pQx+ttp =Q
t\m"tj",{l ,
K= 4x rl EL
J
-(-q)tffi p(r) t,
fi,=
X= ar
a\b L
,d o.rr-27--o X = 1r- rJ".tg ,--
x'- 3u
(x-rf
-3t
3x + ?): O x, ,7.=o xizY+g=A X"3X+9 =O ,F";u xon
a
lYx=@ c.
x4+zxz-3-o
Le* a--Xa
0t,Xq
-3:triE:fl
ac )'
aL
'
A'nac.-3=O
(ar)(&-D = o
(ntDftrD= c $:"3=O Lf x1
r
=Q
X' =l
d. xa
x" 01x'r
Le+ a=
-
Bxz
- :to
qLBa+ lta=C
(a- q)b-q)=C (xq- q)(x1 q) = c
144=O X-=(/
f: tp
{-JT
hqve aJ bon rnr,rl*iplf cit "f a
