Question

Find the polynomial function with the following roots: –2 of multiplicity 2, and 5

Answer 1

is it -2^2=4 and -2^5=32?

Answer 2

no

Answer 3

haha didnt think so

Answer 4

first of all it is a polynomial that will look like \(x^3+bx^2+cx+d\)
if one of the roots is 5 then one of the factors is \(x-5\)

Answer 5

if one of the roots is \(-2\) then a factor is \(x+2\)

Answer 6

and since you are told that \(-2\) is a root with "multiplicy" 2 that means you have a factor of \((x+2)^2\)

Answer 7

meaning the answer is
\[p(x)=(x+2)^2(x-5)\] but your teacher probably wants you to multiply this out

Answer 8

do i foil it then?

Answer 9

lol
yeah "foil" aka multiply out

Answer 10

\[(x+2)(x+2)(x-5)=(x^2+4x+4)(x-5)\] is a start

Answer 11

um lol (x^2+4x)(x-1)?

Answer 12

idk

Answer 13

wait, is it x^3-x^2-16x-20?

Answer 14

you can use the distributive property
A ( x + y) = Ax + A y

where A can be complicated
\[ (x^2+4x+4)(x-5) = (x^2+4x+4)x + (x^2+4x+4)(-5) \]
now distribute again, and combine "like terms"
your answer looks good but I did not check it carefully

Answer 15

okay, thank you!!