Question

can someone plz check my answers
What are the zeros of the polynomial function: f(x) = (x + 3)(x – 1)(x – 5)?

–3, 1, 5

–3, –1, –5

3, 1, –5

3, –1, 5--->MY ANSWER

What is the remainder when (x3 – 59) ÷ (x – 4) ?

5

9 --->MY ANSWER
What are the zeros of f(x) = x3 – 4x2 – 7x + 10 ?

–2, 1, 5

2, –1, –5

–2, 1, –5 --->MY ANSWER

–2, –1, –5


1

6

Answer 1

Not quite ....There are only 3 zeros for the first function. You listed too many.

Answer 2

THe remainder is not 59

Answer 3

so the first one i need to resolve

Answer 4

Again in the last function you have too many zeros.

Answer 5

ok thanks fot letting me know

Answer 6

The first one you got mixed up, set the factors (x + 3)(x – 1)(x – 5) all equal to 0 respectively and you get

x+3=0
x= (-3)

x-1=0
x= (1)

x+5=0
x= (-5)

Basically a factor is just : (x-a) where a is postitive and (x+a) is just equal to (x-(-a))

Answer 7

Yes the zeros of a function are only the values of x that will make the function equal zero.

Answer 8

So Since f(x) = (x+3) (x-1) (x-5) you are looking for what x s make (x+3) (x-1) (x-5) =0

Answer 9

of course that would be either when x +3 = 0 or when x-1 =0 or when x-5 =0.

Answer 10

oh ok i see now i didnt set them equal to zero

Answer 11

So what are your three zeros @countrycuties16

Answer 12

-3,1,5

Answer 13

Bingo

Answer 14

For the second question ... do you know how to do synthetic division?

Answer 15

i am not good at it i really didnt understand it my teacher refuses to explain it to me

Answer 16

ok so for synthetic division you list each of the coefficients of each term (do you know what a coefficient is?)

Answer 17

thee coefficent is x^3?

Answer 18

no the coefficient is the number you multiply the variables by ... in general it is the number in front of the variable so for example...
6x^2-2t +y = 16

6 is the coefficient of x^2, -2 is the coefficient of t and 1 is the coefficient of y.

Answer 19

Notice that I included a negative if it was a substraction like -2 for the t term

Answer 20

oh ok i see so it will be -4

Answer 21

well yes that is one but hold on.

Answer 22

so you take the polynomial that you are dividing (not the one that you are dividing by)...so in this case \[(x^3-59) \div (x-4)\]

Which one are you dividing?

Answer 23

(x^3-59)

Answer 24

right! Now...list all of the coefficients of each term of that polynomial but keep in mind if a term is missing that the coefficient is then 0... so go ahead and list them

Answer 25

so i did that and i got a remaider of 5

Answer 26

There you go! Now you have it.

Answer 27

thanks so much is my last on ok???

Answer 28

one*

Answer 29

Now for the last part you have to do a little bit of everything. First list all possible zeros which you do by taking the constant term and listing all of its factors (both positive and negative and call that set P.

Answer 30

So for example if the function is f(x) = 5x^3 - 4x^2 +5x -8.

Then your set P = {1,2,4,8,-1,-2,-4, -8}

Answer 31

Then find all the factors of the coefficient of the highest degreed term and call those set Q.
In my example that would be Q= {1,5,-1,-5}

Answer 32

Are you following me?

Answer 33

yes i am i am starting to understand

Answer 34

Then to find your possible rational zeros list all combinations of P/Q.

Answer 35

So for my example the possible rational zeros are P/Q={1,2,4,8,1/5,2/5,4/5,8/5,-1,-2,-4, -8, -1/5,-2/5,-4/5,-8/5}. Now that is more than you would usually have but it is an example... If there are any repeats then you can toss the repeats out.

Answer 36

i got -2,1,15 fir my answer

Answer 37

for*

Answer 38

Nope

Answer 39

For your equation f(x) = x^3-4x^2-7x+10 ... What is your set P?

Answer 40

Are you still with me @countrycuties16 ?

Answer 41

yeah sorry i am completel lost

Answer 42

completely*