Polynomial Functions Test 1.f(x) = 4x3 + 11x2 + 5

The relative maximum is at x = –1.83, and the relative minimum is at x = 0.
The relative maximum is at x = –1.83, and the relative minimum is at x = 0.

The relative maximum is at x = –1.83, and the relative minimum is at x = 1.
The relative maximum is at x = –1.83, and the relative minimum is at x = 1.

The relative maximum is at x = 1.83, and the relative minimum is at x = 0.
The relative maximum is at x = 1.83, and the relative minimum is at x = 0.

The relative maximum is at x = 1.83, and the relative minimum is at x = 1.
2. Given a polynomial and one of its factors, find the remaining factors of the polynomial.

x3 + 2x2 − x − 2; x+2
The remaining factors are (x - ) and (x + )
3. Use synthetic substitution or direct substitution to find f(2) for the function f(x) = 3x4 + x3 − 2x2 + x + 12.

f(2) =
4.Find all of the zeros of the function f(x) = x3 + x2 − 17x + 15.

The zeros of the function are -
,
, and
. (Put the zeros in order from least to greatest.)
5. For the given function, determine consecutive values of x between which each real zero is located.

f(x) = –14x4 – 7x3 – 18x2 + 17x + 11

There is a zero between x = 0 and x = 1.
There is a zero between x = 0 and x = 1.

There are zeros between x = 1 and x = 0, x = 0 and x = –1.
There are zeros between x = 1 and x = 0, x = 0 and x = –1.

There are zeros between x = 2 and x = 3, x = 1 and x = 2, x = –1 and x = –2, x = –1 and x = –2, x = –2 and x = –3.
There are zeros between x = 2 and x = 3, x = 1 and x = 2, x = –1 and x = –2, x = –1 and x = –2, x = –2 and x = –3.

There is a zero between x = 0 and x = –1.
6.Find all of the zeros of the function f(x) = x3 + 7x2 + 4x − 12.

The zeros of the function are -
, -
, and
. (Put the zeros in order from least to greatest.)
7.Given a polynomial and one of its factors, find the remaining factors of the polynomial.

2x3 + 7x2 −53x − 28; x−4
The remaining factors are (x +
) and (
x +
)
8. Find all of the zeros of the function f(x) = x4 − 3x3 − 3x2 − 75x − 700.

The zeros of the function are -
,
, -
i, and
i. (Put the zeros in order from least to greatest.)

-14

step-by-step explanation:

2x2 – 2(x+4)

=2x2-2（5+4）

=4-2×9

=4-18

=-14

a) $ 9.50

b) 17

c) y-intercept (0, 12). this is the initial amount of money that joe had prior to playing any game.

d) x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e) slope is -0.5. joe's balance will reduce by 0.5 for every game that he plays.

f)

domain; [0,24]

range; [0,12]

g) x + 2y = 24

step-by-step explanation:

a)

if joe plays 5 games, this will imply that x = 5. substitute x = 5 in the equation and solve for y;

y = -.50x + 12

y = -0.50(5) + 12

y = 9.50

b)

if joe leaves the arcade with $3.50, this will mean that y = 3.50. plug in y = 3.50 in the given equation and solve for x;

y = -.50x + 12

3.50 = -0.50x + 12

0.50x = 12 - 3.50

0.5x = 8.5

x = 17

c)

the function given is   y = -.50x + 12.

the y-intercept is the point where the graph of this function will intersect the y-axis. at this point, the value of x is usually 0. plug in x = 0 in the given equation and determine y;

y = -0.50(0) + 12

y = 12

the y-intercept is thus (0, 12). this is the initial amount of money that joe had prior to playing any game.

d)

the x-intercept refers to the point where the graph of a function intersects with the x-axis. at this point, the value of y is 0. substitute y = 0 in the given equation and solve for x;

0 =   -.50x + 12

0.5x = 12

x = 24

x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e)

the slope of the given equation is -0.5. the equation has been given in slope-intercept form. thus the slope is simply the coefficient of x.

joe's balance will reduce by 0.5 for every game that he plays. this is the interpretation of the slope.

f)

domain is the set of x values for which the function is real and defined. the domain will thus be; [0,24]. this will restrict the balance to only assume positive values.

on the other hand, the range is the set of y values for which a function is real and defined. the range in our case will be [0,12]. joe can have between $0 and $12 balance.

g)

the standard form of the equation of a straight line is;

ax + by = c

where a, b, and c are integers.

our equation is given as;

y = -.50x + 12

re-writing the equation we have;

0.5x + y = 12

divide all through by 0.5;

x + 2y = 24

true

step-by-step explanation:

according to the national european world center, the engineering of the ford company on elon musk's flame throwers proved the globalization of the natural wallabies and therefore, results in the growth product domestication in almonds.

answer: you will have more water.