Question

What polynomial has roots of -5, 2, and 4 ?

Answer 1

the one that looks like
\[(x+5)(x-2)(x-4)\] after you expand

Answer 2

yes

Answer 3

Im guessing im wrong

Answer 4

i would do this
http://www.wolframalpha.com/input/?i=(x%2B5)(x-2)(x-4
and look at "expanded form"

Answer 5

im still confused on this

Answer 6

if \(-5\) is a zero, then one factor has to be \(x+5\)

Answer 7

if \(2\) is a zero then one factor must be \(x-2\) and if \(4\) is a zero then one factor is \(x-4\)

Answer 8

that means in "factored form" the polynomial is
\[(x+5)(x-2)(x-4)\]
if you want it in standard form multiply all that mess out

Answer 9

well im still confused but thank you anyways

Answer 10

i cannot think of another way to say it
if you want to solve \((x+5)(x-2)(x-4)=0\) you would have
\[x+5=0\iff x=-5\\
x-2=0\iff x=2\\
x-4=0\iff x=4\] so the zeros would be \(-5,2,4\)

Answer 11

now you are told the zeros are \(-5,2,4\) so the polynomial you started with must be \[(x+5)(x-2)(x-4)\]