Question

Write a polynomial function in standard form with the given zeros x=-1,-2,-3

Answer 1

(x-2)(x+2)(x+3)

Answer 2

can you do it from here?

Answer 3

(x-2)(x^2+5x+6)

Answer 4

(x^3+5x^2+6x-2x^2-10x-12)
x^3+3x^2-4x-12

tell me what part you were stuck on

Answer 5

How you would write it with the zeros of x=-1,-2,-3? I really do not understand this concept...

Answer 6

Factor-Root Theorem: If (x-k) is a factor of the polynomial, then k is a zero of the function and vice-verse.
e.g. x=-1 is a zero, therefore (x+1) is a factor.

Answer 7

Convert all the zeroes to factors and multiply them all together.

Answer 8

so would it be like x^4+7x+5?? haha (:

Answer 9

Not likely. It could be of higher degree, but best to assume it's a third degree polynomial for simplicity.

Answer 10

(x+1)(x+2)(x+3)

notice if we put in -1,-2, or -3 that whole thing goes to 0

and notice when you solve quadratic equations you start with something like ax^2+bx+c and get it down to some (x-3)(x+2) or something like that. And we stet that = to 0 to get the solutions

what we are doing in your case here is going the other way, we are given the solutions, so we are building the polynomial from the solutions

Answer 11

okay thats understanding... so what i did is wrong right?

Answer 12

What did you do?

Answer 13

so i put (x+1)(x+2)(x+3)... then i multiplied them and got some weird function like x^4+7x+5....?

Answer 14

You can't get x^4 because there are only three x's multiplying.

Answer 15

Start by multiplying two of the binomials, e.g. (x+2)*(x+3) to get a quadratic trinomial in standard form, then distribute in the other factor.

Answer 16

Try following zzrocker's example.

Answer 17

oh yeah thats right! okay let me see what i can do

Answer 18

x^3+6x^2+11x+6????

Answer 19

Is that correct?

Answer 20

That's what I got. You can check it by plugging in one of the given zeroes and see if it works.

Answer 21

okay cool! Thanks to both of you!