Question

Part 1: Find the polynomial f(x) that has the roots of –2, 5 of multiplicity 2. (4 points)

Part 2: Explain how you would verify the zeros of f(x). (4 points)

Answer 1

the root 5 has multiplicity 2
that means the factor is \((x-5)^2\)

Answer 2

close, but the one you wrote has 3 zeros: 2, 5, and -5

Answer 3

"multiplicity 2" means that the factor has a square
that is the "2"

Answer 4

\[(x+2)(x-5)^2\] is what it means i this case

Answer 5

no

Answer 6

it says

5 of multiplicity 2

Answer 7

Ok, so after foiling I get my answer

Answer 8

if you mean "multiply" then yes,
there is no such mathematical operation as "foil"
you have to multiply
\[(x+2)(x-5)(x-5)\] if you want to write it in standard form

Answer 9

me, i would leave it in factored form, but that might not be what your teacher had in mind
they tend to be picky about such thigs

Answer 10

ok, at the risk of repeating myself, what you need is to "multiply"
if you want to call it "foil" ok, but there is no "first outer inner last" when multiplying
\[(x^2-3x-10)(x-5)\]

Answer 11

btw i noticed that again you changed \(x-5\) in to \(x+5\)
it is
\[(x+2)(x-5)(x-5)\]

Answer 12

absolutely

Answer 13

no problem, it is not your fault, i am sure that is what your math teacher called it

Answer 14

yw