Question

Write a polynomial function with the given roots

Answer 1

so before you even type it, what does it mean when you have a root?

Answer 2

Basically the 0 of the polynomial?

Answer 3

yea, it means at that point, y=0

Answer 4

so, what do we know that whenever we multiply by it, we get zero?

Answer 5

So for the polynomial we have to write, y has to equal 0 at 7 AND 10?

Answer 6

Anything multiplied by 0 is 0

Answer 7

yep yep

Answer 8

so now, what's the easiest equation where x=7 that y will equal zero?

Answer 9

I have no idea, that's where I'm stuck

Answer 10

ok, so what's 2-2?

Answer 11

0

Answer 12

ok, how about 7-7?

Answer 13

0

Answer 14

so, at x=7, what will x-7 equal?

Answer 15

0

Answer 16

Ohhh I get it!

Answer 17

right, now stick that in parentheses

Answer 18

(x-7) - (x-10)? Would that work?

Answer 19

can't be subtraction

Answer 20

How do we incorporate the 10?

Answer 21

what function do we know for a fact we can always use to get a zero

Answer 22

hint, I brought it up above

Answer 23

Multiplication? Anything times 0 is 0?

Answer 24

right!

Answer 25

so you were good with the x-10 part

Answer 26

So (x-7)(x-10)?

Answer 27

but not the subtraction sign in the middle

Answer 28

good, now you must have an equals sign

Answer 29

and something on the other side of said equals sign

Answer 30

(x-7)(x-10) = y

Answer 31

yay!

Answer 32

You fixed it yourself :)

Answer 33

Got it! Thanks so much :)

Answer 34

np, you did it!

Answer 35

:D

Answer 36

so, for when you are on a test or something where you can't get help, start by thinking of definitions. What does this mean? What do they want? Once you figure than out, it becomes a lot easier. :) Best of luck! Keep on learning!

Answer 37

Alright, thank you for the helpful advice :)