Question

4.
Use the “zero” utility of your calculator to determine the zeros of
f(x) = x^2 + 5x - 10 (round to the nearest tenth if necessary).

5. What are the zeros of the polynomial f(x) = x^4 (x-2)^2
(x+1)? Tel whether each zero is odd or even.

7. Use synthetic division to determine if k = -3 is a zero of
f(x) = 2x^3 + 13x ^2 + 30x + 25. Give the answer as “yes” or “no”.
Show your work

8.) Use synthetic division to determine if x-1 is a factor of
x^3 + 4x^2 + x - 6. Give the answer as “yes” or “no”. Show your
work

Answer #1

1) Given function is f(x) = x^{2} + 5x - 10

Now, f(x) = 0 gives, x^{2} + 5x - 10 = 0

i.e., x =

i.e., x =

i.e., x =

i.e., x 1.5, -6.5

Therefore, the zeros of the given function are 1.5 and -6.5

2) Given function is f(x) =
x^{4}(x-2)^{2}(x+1).

Now, f(x) = 0 gives, x^{4}(x-2)^{2}(x+1) = 0

i.e., x =0,-1,2

Here 0,2 are even zeros and -1 is odd zero.

3) We have to check here whether x = -3 is a zero of f(x) =
2x^{3}+13x^{2}+30x+25 or not.

Putting x = -3 in the given function we get, f(-3) =
2(-3)^{3}+13(-3)^{2}+30(-3)+25

i.e., f(-3) = -54+117-90+25

i.e., f(-3) = -2

Therefore, -3 is not a zero of the given function.

4) We have to check here whether x-1 is a factor of f(x) =
x^{3}+4x^{2}+x-6 or not.

Dividing f(x) by x-1 we get,
(x^{3}+4x^{2}+x-6)/(x-1) = x^{2}+5x+6 and
there is no remainder.

Therefore, x-1 is a factor of the given function.

You will need to use the rational zero test to find all the
possible rational zeros, along with synthetic division to find the
actual zeros of the function. f(x)=-2x^3-7x^2+14x-5

1.Determine all the zeros and their multiplicities of the
polynomial function f(x) = x 5 − 6x 3 + 4x 2 + 8x − 16
2. Find all the zeros of the function f(x) = x 5 − 4x 4 + x 3 −
4x 2 − 12x + 48 given that −2i and 4 are some of the zeros.

1. Let f(x)=−x^2+13x+4
a.Find the derivative f '(x)
b. Find f '(−3)
2. Let f(x)=2x^2−4x+7/5x^2+5x−9, evaluate f '(x) at x=3 rounded
to 2 decimal places.
f '(3)=
3. Let f(x)=(x^3+4x+2)(160−5x) find f ′(x).
f '(x)=
4. Find the derivative of the function f(x)=√x−5/x^4
f '(x)=
5. Find the derivative of the function f(x)=2x−5/3x−3
f '(x)=
6. Find the derivative of the function
g(x)=(x^4−5x^2+5x+4)(x^3−4x^2−1). You do not have to simplify your
answer.
g '(x)=
7. Let f(x)=(−x^2+x+3)^5
a. Find the derivative....

f(x)=x^3+8x^2+14x+4 (given that -2 is a zero)
find all zeros of the polynomial function

A20) Given that f(x) is a cubic function with
zeros at −2−2 and 2i−2, find an equation for f(x) given that
f(−7)=−6
B19) Find a degree 3 polynomial whose coefficient
of x^3 equal to 1. The zeros of this polynomial are 5, −5i, and 5i.
Simplify your answer so that it has only real numbers as
coefficients.
C21) Find all of the zeros of P(x)=x^5+2x^3+xand
list them below with zeros repeated according to their
multiplicity.
Note: Enter the zeros as...

Verify the quotient rule for each of the following:
1. f(x)=4x^5-4x^4+13x^3-2x^2+7x+6/x^2-x+2
2. f(x)=20x^8-28x^6+29x^4-35x^2+5/5x^4-7x^2+1

find all real zeros if the function P(x)=2x^4-x^3-4x^2+10x-4
i know all possible zeros are + or - 1, +- 1/2, +-2, +-4
im not sure how to do this and show the work

3. Write the zeros of the polynomial below and indicate the
multiplicity of each zero. What is the degree of the polynomial?
Describe the end behaviors of the graph. Make a sketch of this
function. Your sketch should be neat, showing your zeros and where
the graph touches or cross the x-axis and the end behaviors. Please
show your work!!
f (x) = (x- 5)2 (x+ 2)2 (x- 1)
Degree: ________________
Zeros/Multiplicity: __________________
End Behaviors: LH___________________
RH___________________

Function: H(x)= 7x^3-117x^2+535x-325
A. Use Rational Zeros Theorum to find all possible rational
zeros.
B. Find the actual rational zero and prove it is zero by using
synthetic division.
C. Find the remaining zeros.
D. Factor H(x) completely into linear factors.

The fourth degree polynomial x^4-5x^3+5x^2+5x-6 has four
different zeros. If two of the zeros are 1 and 2, what are the
other two zeros?

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