## Transcribed Text

(1 point) Suppose f ( x) = x5 ( 5 - 2x3 ).
(a) The roots of f ( x) are x = O, 1.35720880
Is repeated , enter lt only once .)
(b) As X -+ 00 , f (x) -+
(b) As X -+ - 00, J (x) -+
help (numbers) (lf a root
help (numbers)
help (numbers)
(1 point) For the tunction y = ( x - 3) (x + 2) ( 4x - 2),
its y-i ntercept is y =
its X-intercepts are X =
Note: lf there is more than one answer enter them separated by commas . lf there are
none , enter none .
When X -+ 00, y -+ oo ( Input + or - for the answer )
When X -+ -00, y -+ oo ( Input + or - for the answer )
(1 point) Use synthetic division and the Remainder Theorem to evaluate P( e), where
P (x) = x3 -3 x2 + 6x -14 , c = 2
The quot ient is [ l
(1 point) Use synthetic division and the Remainder Theorem to evaluate P( e), where
P( x) = x2 + 8x + 9, e = -1.
°The quot ient is
(1 point) Use synthetic division and the Remainder Theorem to evaluate P( e), where
P(x) = x 4 + 7x3 + 3x 2 + 24x + 22, e= -7
th e quotient is
(1 polnt) For the functlon y = l X - ti) l x + O),
its y-i ntercept is -48
its X-intercepts are X = 8, -6
Note: lf there Is more than one X- lntercept wrlte the x-values separated by
commmas.
When X -+ 00, y -+
When X -+ -00, y -+
00 (Input + or - for the answer)
00 (Input + or - for the answer)
(1 polnt) What Is the degree of the followlng polynomlal?
(x3a - l)( x3ª + 3)
Degree:
(1 point) The potynomiat f ( x) = ( 4 - 2x )(3x - 3)2
has
degree= -3 ----- teadlng coeff lclent= --18- ---- constant coeff lclent= 1
(1 point) The potynomiat f ( x) = x5 ( 5 - 2x3 ) has
degree= 8
teadlng coeff lclent= -2
constant coeff lclent=
(1 point) Suppose f(x) = ( 4 - 2x)(3x - 3)2
.
(a) The roots of f (X) are X = ¡ 2, 1 J help (numbers) (lf a root ~------~
is repeated , enter it only once .)
(b) As X --+ 00, f(x) --+ help (numbers)
(b) As X --+ -oo, f (X) --+ ~------~ help (numbers)
(1 point) Suppose f(x) = - (3 - x)(x + 2)(5x + 2)2.
(a)Therootso f f(x) are x = 3,-2,-215
is repeated , enter it only once.)
(b) As X --+ 00, f (x) --+
(b) As X --+ -00, f (x) --+
help (numbers) (lf a root
help (numbers)
help (numbers)
(1 point) Find the quotient and remainder using synthetic division for
x5
- x4 + 8x3
- 8x2 + 2x - 10
x-1
The quotien t is
(1 polnt) Flnd a degree 3 polynomla l having zeros -3, 4 and 8 and the coefflcle nt of
x 3 equal 1.
The polynomlal Is
(1 point) Ust ali possible rational roots for the function
f(x) = 7x4 + 5x3 + Ox2
- 9x + 91.
Give your list in increasing order. Beside each poss ible rational root, type "yes· if it is
a root and · no· if it is nota root. Leave any unnecessary answer blanks empty.
Possible rational root: - Is it a root? 11 1 . Possible rational root: Is ita root? - Possible rational root: Is ita root? - Possible rational root: Is ita root? - Possible rational root: Is ita root? - Possible rational root: Is ita root? - Possible rational root: Is ita root? - Possible rational root: Is ita root? - Possible rational root: Is ita root? - Possible rational root: Is ita root? - Possible rational root: Is ita root? - Possible rational root: Is ita root?
(1 point) Find all the real zeros of the polynomial
P(x) = x3
- 2x2
- 9x + 4.
Enter the real zeros as a comma -separated list:
14,-1 + sqrt(2), -1- sqrt(2)
Note: Give exact answers; no decimals. lf needed, enter square root as sqrt, e.g. the
square root of 2 should be enterad as sqrt(2).
When x --> oo, P( x) --> 1 ---.------""--,
When x --> -oo, P( x) -->
Note: lf your answer is oo, enter infinity; if your answer is -oo, enter -infinity.
(1 point) Find the quotient and remainder using synthetic division for
x5
- x4 + 3x3
- 3x2 + 9x - 16
x - 1
The quotient is "'----------
( 1 polnt) Glven that f ( x) Is a cublc functlon wlth zeros at - 6, 2, and 9, flnd an
equatlon for f (x ) given that / (- 5) = 9.
f( x) =
(1 polnt) Flnd a degree 3 polynomlal whose coefflclent of x3 equal to 1. The zeros of
thls polynomlal are 1, - 2i, and 2i. Slmplify your answer so that it has only real
numbers as coeffic ients.
Your answerIs
(1 point) Find a degree 3 poly nomial that has zeros - 2, 3 and 8 and in which the
coeffic ient of x 2 is -18.
The polynomial is
(1 point) For
p(x) = 1.5 + x1 + 3x2 + 7x3 + 2x4 + 8x5 + 8x6
Degree of p =
Leading term =
Leading coefficien
6
8X"6
t = 8
Determine the coefficient and the degree of each term.
Term Coefficient Degree
1.5
X
3x2
7x3
2x4
8x 5
8x6
l O
A B
l O
' '
e o
1. f(x) = (x - l)(x - 3)(x - 5)
2. f(x) = (x - l)(x - 3)(x + 5)
3. f(x) = (x - l)(x + 3)(x + 5)
4. f(x) = (x + l )(x + 3)(x + 5)
.
.
1 /1 (\
• . •
• .. • ...
J . . . . \
A B
I ,
.
•
' '
J• V
.
e D
e 1.f( x) = - x3 + x2 + 6x
a 2. f( x) = - x3 - x2 + 6x
d 3 . f ( x) = x3 - x2 - 6x
b 4 . f ( x) = x 3 + x 2
- Gx
[
•••
A B
•• • ••
e D
d 1. J(x) = x4 + 5x2 + 4
a 2.f(x) = x4 - 5x2 +4
b 3. J(x) = -x 4 + 5x2 - 4
e 4.f(x) = -x 4 -5x 2 - 4
(1 point) For the tunction y = ( x - 2) (x + 2) (6x - 2),
its y-i ntercept is y =
its X-intercepts are X =
Note: lf there is more than one answer enter them separated by commas. lf there are
none, enter nona .
When X -+ 00, y -+ oo ( Input + or - for the answer )
When X -+ -00, y -+ oo ( Input + or - for the answer )
(1 point) For the tunction y = x4 - 5x 3 - 14x2,
its y-i ntercept is y = .._ _______ ___,
its X-intercepts are X =
Note: lf there is more than one answer enter them separated by commas. lf there are
none, enter nona .
When :t -+ oo, y -+ oo (Input + or - tor the answer)
When :t -+ -oo, y -+ oo (Input + or - tor the answer)
(1 point) Let
f(x) = x2 + 2x + 3 and g(x) = 4x3
- 5x2 + 4x + 1
For brevity let's write deg(p) for the degree of a polynomial p. So in the above
example, deg(f) = 2 and deg(g) = 3. You can answer the follow ing questions
without actually computing the indicated functions .
deg(f + g)
deg(f - g)
deg(f g)
deg(f o g)
deg(g o f)
(1 point) For the function y = ( x - 1 )2( x - 6),
its y-intercept is y =
its X-i ntercepts are X =
Note: lf there is more than one answer enter them separated by commas. lf there are
nona, enter nona .
When X --> 00, y --> oo ( Input + or - for the answer )
When X --> -00, y --> oo ( Input + or - for the answer )
(1 point) For the tunction y = x 3 - x 2 - 12x,
its y-i ntercept is y =
its X-i ntercepts are X =
Note: lf there is more than one answer enter them separated by commas. lf there are
none, enter nona .
When X -+ 00, y -+ oo ( Input + or - for the answer )
When X -+ -00, y -+ oo ( Input + or - for the answer )
(1 point) For the tunction y = x 4
- 5x3 - 24x2,
its y-i ntercept is y =
its X-i ntercepts are X =
Note: lf there is more than one answer enter them separated by commas. lf there are
none, enter nona .
When X -+ 00, y -+ oo (Input + or - tor the answer)
When X -+ -oo, y -+ oo (Input+ or - tor the answer)
(1 point) For the tunction y = x3 - x 2 - 12x,
its y-i ntercept is y =
its X-i ntercepts are X =
Note: lf there is more than one answer enter them separated by commas. lf there are
none, enter nona .
When X -+ 00, y -+ oo ( Input + or - for the answer )
Whenx -+ -oo, y-+ oo ( Input + or - for the answer )
(1 point) For the function y = x( X - 7) (X+ 6),
its y-intercept is y =
its X-i ntercepts are X =
Note: lf there is more than one answer enter them separated by commas. lf there are
none, enter none .
When X -+ 00, y -+ oo ( Input + or - for the answer )
When X -+ -00, y -+ oo ( Input + or - for the answer )
(1 polnt) The polynom lal of degree 4, P( x) has a root of multlpllcity 2 at :i; = 4 and
roots of multip licity 1 at X = O and X = -4. lt goes through the point ( 5, 4.5}
Find a formula for P( X).
P(x) =
(1 point) Find the quotient and remainder using long dlvision for
2x3
- 8x2 + 7 x - 13
2x2 + 5
The quotlent Is

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