Question

Find all zeros of the function given one of the zeros


f(x)=15x^3-119x^2-10x+16;8

Answer 1

Sorry its find all real zeros of the function

Answer 2

Have you considered Synthetic Division?

Answer 3

yes i did it

Answer 4

I got 15x^3-7x^2-66x+518/x+8

Answer 5

how do i find all the zeros?

Answer 6

@Callisto @ganeshie8 @Gravityy.boyy @hartnn

Answer 7

if you have a zero, it will divide evenly into the polynomial (no remainder)

in other words, for a cubic P(x), you would expect
P(x)= (x-a)(x-b)(x-c)
(in factored form)
if you know c is a root, and divide by (x-c)
you get
(x-a)(x-b)
(but in expanded form)

Answer 8

i got 8,-6,5 for the zeros is that correct?

Answer 9

what did you get after dividing by (x-8) ?

Answer 10

15x^2+x-2

Answer 11

and then that factored out to( x+6)(x-5)

Answer 12

15x^2+x-2 looks good

but (x+6)(x-5) = x^2 + x -30

Answer 13

how would u factor 15x^2+x-2?
I times 15 times -2 and then did the factoring...

Answer 14

yes, the "a" coefficient not being 1 is a pain.
I do the same thing as you, -2*15= -30
list the pairs of numbers that multiply to give 30
1,30
2,15
3,10
5,6

notice the sign of -30 means "opposite signs"
notice the + sign on +x means the bigger number is +
test which pair adds to +1:
-5+6 = 1 so 5,6 is the pair.

Now, because "a" is not 1, I look for the number in the pair that divides into a=15
5 does, and we get 3
that tells me (3x ) is one of the factors. also, divide 3 into 15 to get 4 5 for the other factor

(3x ) (5x )
next, we need to get a -5 and a +6, so fill in the blanks.
(3x -1) (5x ) (the -1 * 5x gives -5x)
(3x -1)(5x +2) (gives +6x)

Answer 15

**also, divide 3 into 15 to get 5x for the other factor

Answer 16

now solve
(3x -1)(5x +2)=0

Answer 17

ok i get it thanks... i need help on anothquestion...

Answer 18

factor the polynomial: 2x^3+16y^3

Answer 19

i know im supposed to use (a+b)(a^2-ab+b^2)

Answer 20

the first thought is factor out a 2
\[ 2(x^3 + 8y^3)\]

the 2nd thought is 8 = 2^3, so this is the same as
\[2( x^3 +(2y)^3)) \]

Answer 21

now you can use your expression, with a= x and b = 2y

Answer 22

so its (x+2y)(x^2-2yx+2y^2)

Answer 23

(it's not its)
but with a leading 2 ... from 2(x^3 + (2y)^3)

Answer 24

and the last term in parens is (2y)^2 = 4y^2 (not 2y^2)

Answer 25

wait so i multiply the four by each one?

Answer 26

(a^3+b^3) factors into (a+b)(a^2-ab+b^2)

and
2(a^3+b^3) = 2(a+b)(a^2-ab+b^2)

now replace a with x and b with 2y
2(x^3 + 8y^3) =2(x + 2y) ( x^2 -x*2y + (2y)^2 )
or
2x^3 +16y^3= 2(x+2y)(x^2 -2xy +4y^2)

Answer 27

ohhhi get it could u please help me with polynomial long division?

Answer 28

please make it a new post.