If x = 1 is a zero of the polynomial function f(x) = 3x3 − 8x2 + 3x + 2, which of the following is another zero of f(x)?
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- anonymous

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- schrodinger

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- anonymous

@welshfella @WazapxD @Michele_Laino

- anonymous

wouldnt be a x behind 2

- anonymous

4x^3-8x^2+3x+2

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## More answers

- anonymous

ima work this out brb

- anonymous

ok

- anonymous

whats the answer choices

- anonymous

(x-2) (3x+1) (x-1) are the factors of the polynomial function

- anonymous

sets of zeroes are x=2 x= -1/3 x=1

- anonymous

The answer choices are 2, -2, -1, 5

- anonymous

it is 2

- anonymous

how?

- anonymous

you need to factor the trinomial function to find the zeroes

- anonymous

but wouldn't it be -1,2, and 1/3

- anonymous

yes that is correct
they're 3 zeroes in a cube root unless one of the zeroes is repeated

- anonymous

they are only looking for another one

- anonymous

which is 2 or -1/3 since 1 is given

- anonymous

ok. can i ask another?

- anonymous

yes

- anonymous

Anyone?

- welshfella

this is the Descartes rule of signs which i've only got a vague memory of . I'll see if I can find a website for you. Or maybe someone who remembers it will come along..

- anonymous

Here is a link to a similar question

- anonymous

But I still don't understand it :(

- welshfella

http://www.purplemath.com/modules/drofsign.htm

- anonymous

:) Thank you!!

- anonymous

Which polynomial identity will prove that (3 + 6)2 = 81?

- anonymous

power rule

- welshfella

there are 3 changes of sign in this polymomial

- anonymous

so would it be difference of squares?

- anonymous

Square of a Binomial

- anonymous

Which of the following is a polynomial with roots: −square root of 3, square root of 3, and −2?

- welshfella

now you find f(-x) and count the sign changes again
f(-x) = (-x)^6 −(- x)^5 − (-x)^4 + 4(-x)^3 − 12(-x)^2 + 12
= x^6 + x^5 - x^4 - 4x^3 -12x^2 + 12
- 2 changes of signs

- anonymous

So for the positive would it be 4,2,0 sign changes?

- welshfella

i missed one out for f(x) its 4 sign changes

- welshfella

not sure - i'll have to re check

- anonymous

Ok. So would the answer be positve:4,2,0 and negative 2,0 and complex:6,4,2,0

- welshfella

yea 4,2 or 0 positive roots

- anonymous

Which of the following is a polynomial with roots: −square root of 3, square root of 3, and −2?

- anonymous

x3 − 2x2 − 3x + 6
x3 − 3x2 − 5x + 15
x3 + 2x2 − 3x − 6
x3 + 3x2 − 5x − 15

- anonymous

is the answer B?

- welshfella

yes i think you are right for the first one

- anonymous

so is it B for the second question?

- welshfella

roots sqrt3 - sqrt3 and -2
factors will be
(x + 2)(x - sqrt3)(x + sqrt3)
= (x +2)(x^2 - 3)

- welshfella

expanding gives
x^3 + 2x^2 - 3x - 6

- anonymous

So it would be A?

- welshfella

that is C

- anonymous

really?

- anonymous

x3 + 2x2 − 3x − 6

- anonymous

That one?

- welshfella

yes

- anonymous

I thought it was A. But i believe u

- anonymous

What is the quotient (6x4 − 15x3 + 10x2 − 10x + 4) ÷ (3x2 + 2)?

- anonymous

2x2 − 5x + 2 I got this as an answer

- anonymous

yes?

- welshfella

sorry I got called away
lets see

- anonymous

It's okay:)

- anonymous

What is the quotient (6x4 − 15x3 + 10x2 − 10x + 4) ÷ (3x2 + 2)?
Just in case u needed the question again

- welshfella

yes

- welshfella

looks good

- anonymous

Was I right?

- welshfella

lol - i'm really slow with this one

- anonymous

it's fine:)

- welshfella

Yes you are right

- anonymous

ok
Using synthetic division, what is the quotient (2x3 − 2x − 12) ÷ (x − 2)?

- anonymous

I got this as an answer: 2x2 + 4x + 6

- welshfella

correct

- anonymous

ok
If x = 1 is a zero of the polynomial function f(x) = 3x3 − 8x2 + 3x + 2, which of the following is another zero of f(x)?

- anonymous

i got -1

- welshfella

f(-1) = -3 - 8 - 3 +2 = -12 so its not -1
as the last term is + 2 it might be -2 or 2

- anonymous

both -2, and 2 are answer choices :(

- welshfella

try f(2)

- welshfella

f(2) = 3(8)- 8(4) + 6 + 2 = 24 - 32 + 8 = 0

- welshfella

so its 2

- anonymous

What is the remainder when (3x4 + 2x3 − x2 + 2x − 24) ÷ (x + 2)?

- anonymous

Thank-you:) For this one I got 0 as a answer

- welshfella

you should really be submitting them in different posts ..
but ill do this last one

- anonymous

Oh okay. I'm sorry :)

- welshfella

f(-2) will give you the remainder

- anonymous

so it's not 0?

- welshfella

3(-2)^4 + 2(-2)^3 - (-2)^2 - 4 - 24
= 48 - 16 - 4 - 4 - 24 = 48 - 48 = 0

- welshfella

correct

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