Question

consider the polynomial function f(x)=x^3-5x^2-12x+36.

A) given that f(2)=0, find the other zeros of f.
B)Based on your results from part a , what are the factors of the polynomial x^3-5x^2-12x+36
c) what are the solutions of the polynomial equation x^3-5x^2-12x+36=0

Answer 1

Given A) that means you can factor out (x-2) from x^3-5x^2-12x+36.

Answer 2

then you can factor the result of that to determine what other 0's exist.

Answer 3

ok

Answer 4

so wat do i do next

Answer 5

@sweetburger

Answer 6

Or what I would do is divide x-2 off of x^3-5x^2-12+36, since x-2 is a root of the equation (f(2)=0)

Answer 7

You can use synthetic division for this.

Answer 8

ok wait ill do it

Answer 9

You can use synthetic division for this.

Answer 10

ok so i got x^2-7x-26

Answer 11

Okay, solve that equation to find the other zeroes.

Answer 12

how would i do that

Answer 13

You can use the quadratic equation: \[x=-b \pm \sqrt{b^2-4ac} \] all over 2a

Answer 14

ok

Answer 15

ok i got 7+ or - the square root of 153 divide 2

Answer 16

Okay, I don't think that equation is correct earlier, the x^2-7x-26. Did you do your division correctly?

Answer 17

Because when I did the division, I got x^2-3x-18=0.

Answer 18

Check your division.

Answer 19

ok

Answer 20

-5-2 is -7 not -3

Answer 21

The division your not dividing by -2, your dividing by 2.

Answer 22

ok so i did it wrong and now i got wat u got and then i did the quadratic formula and got 3+of - 9 divide 2

Answer 23

You can simplify that answer, two answers are given. (3+9)/2 and (3-9)/2

Answer 24

ok i will do that

Answer 25

x=6 and x=-3

Answer 26

Okay, the zeroes are: 2(given zero), 6, and -3.

Answer 27

A would be the two roots, 6 and -3.

Answer 28

k

Answer 29

so wat would i do to find b

Answer 30

The factors are the zeroes, but subtracting where (x-q) would be a factor, q would be the root.

Answer 31

For example, one of the given roots were 2. A factor form would be (x-2).

Answer 32

What would be the other two?

Answer 33

ok im confused

Answer 34

Lets say you want to factor x^2-4x+4

Answer 35

k

Answer 36

First, you would need to know the zeroes, which would be -2.

Answer 37

so wat would i do

Answer 38

You have to put the equation in the form (x-q)(x-r)(x-s)

Answer 39

Where q r and s are the zeroes of the equation.

Answer 40

ok so (x-2)(x-6)(x--3)

Answer 41

Yes.

Answer 42

ok so i just multiply them

Answer 43

No, multiplying them will give you your original equation.

Answer 44

You leave it like that.

Answer 45

for part b?

Answer 46

Yes.

Answer 47

ok then wat would i do for part c

Answer 48

Part C is asking you for the zeroes, which we've already found. What would they be?

Answer 49

2,6,3

Answer 50

2,6,-3 you mean.

Answer 51

yea

Answer 52

yea, those would be the roots.

Answer 53

ok thanks

Answer 54

your welcome