Question

How do I do this?
Find the polynomial function with roots 1, -2, and 5

Answer 1

(x-1)(x+2)(x-5)

Answer 2

done

Answer 3

Is that really all you have to to do?

Answer 4

you can expand it if you want

Answer 5

yes

Answer 6

that is a polynomial with the roots that you are looking for

Answer 7

How do you expand it?

Answer 8

well what is (x-1)(x+2)

Answer 9

can you solve this?

Answer 10

yes no maybe?

Answer 11

Yes x^2+x-2

Answer 12

ok what is (x-5)(x^2+x-2)

Answer 13

its the same thing as before only you multiply x by the three things inside the brackets then you multiply -5 by the three things inside the brackets

Answer 14

you can multiply these in any order but just do them 1 step at a time and dont be intimidated :)

Answer 15

x^3-4x^2-7x+10

Answer 16

So is that the whole answer?

Answer 17

https://www.wolframalpha.com/input/?i=%28x-1%29%28x%2B2%29%28x-5%29

Answer 18

yeah it is

Answer 19

Thank you so much!!

Answer 20

but you could have kept it like it was unless your teacher tells you to expand

Answer 21

Ok thanks so much I totally understand it now!

Answer 22

There are variations of this problem as well so be aware

Answer 23

that you will have to expand it for those types of problems and then think of what you can multiply by the entire polynomial to manipulate it into what you want it to be

Answer 24

for example if it asks for a leading coefficient of -4

you would have to multiply the entire thing by -4

-4(x^3-4x^2-7x+10)

to give you -4x^(3) in the solution

Answer 25

ok thanks!