Question

Please Explain
Write a polynomial function for the set of zeros:
x=-3,4,7

Answer 1

Well since all of those x's are zeroes, you can write equations for each of them and then multiply them together to get the polynomial

Answer 2

do you know how to write expressions for each of the roots?

Answer 3

Still dont get it... no i dont know how to

Answer 4

okay. So to write an equation for a root you write in the form (x-y) where y is the root.

Now try to write expressions for all of the other roots.

Answer 5

??? so it'd be (x+3) for the first one and then i would set it equal to zero?

Answer 6

It would be like that but remember they are expressions so they won't be set equal to anything

Answer 7

If you know how to solve quadratic equations by factoring you know that you have to set the expression in the parentheses equal to zero to get your root. This is like that, but in reverse. (If you don't know how to do that just don't bother)

Answer 8

can you give me an example of how it would be done?

Answer 9

so if you have the roots x=3,4,5,-6 then the expressions would be (x-3), (x-4), (x-5), and (x+6). To find an equation with all of the x-values as roots, then you would multiply the expressions together and expand

Answer 10

So with my example 1 possible equation would be (x-3)(x-4)(x-5)(x+6).

(I didn't bother expanding this because it would take a long time.)

Answer 11

Ok thank you i think i get what you mean know thanks :)

Answer 12

So what would the answer be?

Answer 13

can i ask one more question?

Answer 14

Sure.

Answer 15

if it tells me to expand the binomial of (1-2x)^2 would i repeat the equation in parenthesis twice and then foil?

Answer 16

Yes. By foil do you mean first outside inside last? I'm pretty sure that's what it means. I don't use that method. I just distribute.

Answer 17

yea thats what it means. so back to the first question i have them set in the paranthesis and now i should foil like im supposed to do in the second question right? then add like terms and i should get my equation

Answer 18

Yes. (1-2x)(1-2x). Then just FOIL and add like terms

Answer 19

no i meant for the first question i asked

Answer 20

the (x+3) (x-4) (x-7)

Answer 21

Oh yeah. Well then: (x+3)(x-4)(x-7). FOIL the first 2 expressions then add like terms. Then FOIL with the last expression. You just be FOILing a quadratic with a linear expression to get a cubic expression which is your answer

Answer 22

Any other questions?

Answer 23

no but can i check back in with you to check my answer?

Answer 24

x^3-8x^2-5x+84 is what i got

Answer 25

This is right.